@prefix dbpedia-owl: .
@prefix dbpedia: .
dbpedia:David_Eppstein dbpedia-owl:knownFor dbpedia:Graph_theory .
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dbpedia:David_Eppstein ns2:knownFor dbpedia:Graph_theory .
@prefix dbpprop: .
dbpedia:David_Eppstein dbpprop:knownFor dbpedia:Graph_theory .
dbpedia:Graph dbpprop:disambiguates dbpedia:Graph_theory .
dbpedia:Kenneth_Appel dbpprop:fields dbpedia:Graph_theory .
dbpedia:David_Shane_Gunderson dbpedia-owl:knownFor dbpedia:Graph_theory ;
ns2:knownFor dbpedia:Graph_theory ;
dbpprop:knownFor dbpedia:Graph_theory .
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dbpedia:Graph_theory rdf:type opencyc:Mx4rvVi3_JwpEbGdrcN5Y29ycA .
@prefix owl: .
dbpedia:Graph_theory owl:sameAs opencyc:Mx4rvt3YbJwpEbGdrcN5Y29ycA ,
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@prefix ns7: .
dbpedia:Graph_theory owl:sameAs ns7:Mx4rvt3YbJwpEbGdrcN5Y29ycA .
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dbpedia:Graph_theory foaf:page ns9:Graph_theory ;
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dbpedia:Graph_theory dbpprop:reference ns10:graph-theory ,
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@prefix rdfs: .
dbpedia:Graph_theory rdfs:label "Grafteori"@no ,
"Teoria graf\u00F3w"@pl ,
"Teorie graf\u016F"@cs ,
"\u00C7izge Kuram\u0131"@tr ,
"\u0422\u0435\u043E\u0440\u0456\u044F \u0433\u0440\u0430\u0444\u0456\u0432"@uk ,
"Graafiteoria"@fi ,
"Grafentheorie"@nl ,
"Teoria dos grafos"@pt ,
"Grafteori"@sv ,
"Teoria de grafs"@ca ,
"\u30B0\u30E9\u30D5\u7406\u8AD6"@ja ,
"Gr\u00E1felm\u00E9let"@hu ,
"Teor\u00EDa de grafos"@es ,
"\u0422\u0435\u043E\u0440\u0438\u044F \u0433\u0440\u0430\u0444\u043E\u0432"@ru ,
"Graph theory"@en ,
"Th\u00E9orie des graphes"@fr ,
"Graphentheorie"@de ,
"\u56FE\u8BBA"@zh ,
"Teoria dei grafi"@it ;
dbpedia-owl:thumbnail ;
dbpprop:abstract "\u30B0\u30E9\u30D5\u7406\u8AD6\uFF08\u30B0\u30E9\u30D5\u308A\u308D\u3093\u3001Graph theory\uFF09\u306F\u3001\u6570\u5B66\u306E\u4E00\u5206\u91CE\u3002\u30CE\u30FC\u30C9\uFF08\u7BC0\u70B9\u30FB\u9802\u70B9\u3001\u82F1\u8A9E\uFF1Anode\uFF09\u306E\u96C6\u5408\u3068\u30A8\u30C3\u30B8\uFF08\u679D\u30FB\u8FBA\u3001\u82F1\u8A9E\uFF1Aedge\uFF09\u306E\u96C6\u5408\u3067\u69CB\u6210\u3055\u308C\u308B\u30B0\u30E9\u30D5\u306E\u6027\u8CEA\u306B\u3064\u3044\u3066\u7814\u7A76\u3059\u308B\u5B66\u554F\u3067\u3042\u308B\u3002\u306A\u304A\u300C\u30A8\u30C3\u30B8\u300D\u3092\u30EA\u30F3\u30AF\uFF08\u82F1\u8A9E\uFF1Alink\uFF09\u3068\u3044\u3046\u5834\u5408\u3082\u3042\u308B\u3002 \u30B3\u30F3\u30D4\u30E5\u30FC\u30BF\u306E\u30C7\u30FC\u30BF\u69CB\u9020\u3001\u30A2\u30EB\u30B4\u30EA\u30BA\u30E0\u306A\u3069\u306B\u5E83\u304F\u5FDC\u7528\u3055\u308C\u3066\u3044\u308B\u3002"@ja ,
"La th\u00E9orie des graphes est une branche commune \u00E0 l'informatique et aux math\u00E9matiques \u00E9tudiant les graphes et les objets qui lui sont propres, comme par exemple les chemins. Le concept de graphe, \u00E0 ne pas confondre avec le graphe d'une fonction, permet d'\u00E9tudier les propri\u00E9t\u00E9s de certaines structures comme les r\u00E9seaux ou, plus largement, les relations binaires. Les algorithmes de la th\u00E9orie des graphes ont ainsi de nombreuses applications importantes. Enfin, la nature particuli\u00E8re des relations entre les objets de cette th\u00E9orie, ou les propri\u00E9t\u00E9s structurelles qu'elle r\u00E9v\u00E8le, ont influenc\u00E9 consid\u00E9rablement l'optimisation combinatoire."@fr ,
"\u00C7izge kuram\u0131, \u00E7izgeleri yani graflar\u0131 inceleyen matematik dal\u0131d\u0131r. \u00C7izge u\u00E7lar ve bu u\u00E7lar\u0131 birbirine ba\u011Flayan kenarlardan olu\u015Fan bir t\u00FCr a\u011F yap\u0131s\u0131d\u0131r."@tr ,
"Die Graphentheorie ist ein Teilgebiet der Mathematik, das die Eigenschaften von Graphen und ihre Beziehungen zueinander untersucht. Dadurch, dass einerseits viele algorithmische Probleme auf Graphen zur\u00FCckgef\u00FChrt werden k\u00F6nnen und andererseits die L\u00F6sung graphentheoretischer Probleme oft auf Algorithmen basiert, ist die Graphentheorie auch in der Informatik, insbesondere der Komplexit\u00E4tstheorie, von gro\u00DFer Bedeutung. Die Untersuchung von Graphen ist auch Inhalt der Netzwerktheorie. Zahlreiche Alltagsprobleme lassen sich mit Hilfe von Graphen modellieren."@de ,
"Teoria graf\u00F3w to dzia\u0142 matematyki zajmuj\u0105cy si\u0119 badaniem w\u0142asno\u015Bci graf\u00F3w. Rozwijanie algorytm\u00F3w wyznaczaj\u0105cych pewne w\u0142a\u015Bciwo\u015Bci graf\u00F3w jest jednym z bardziej znacz\u0105cych p\u00F3l dzia\u0142ania informatyki. Algorytmy te stosuje si\u0119 do rozwi\u0105zywania wielu zada\u0144 praktycznych, cz\u0119sto w dziedzinach na poz\u00F3r nie zwi\u0105zanych z grafami."@pl ,
"A Teoria dos Grafos \u00E9 um ramo da matem\u00E1tica que estuda as rela\u00E7\u00F5es entre os objetos de um determinado conjunto. Grafo \u00E9 uma estrutura G(V,A) onde V \u00E9 um conjunto n\u00E3o vazio de objetos denominados v\u00E9rtices e A \u00E9 um conjunto de pares n\u00E3o ordenados de V, chamado arestas. Dependendo da aplica\u00E7\u00E3o, arestas podem ou n\u00E3o ter dire\u00E7\u00E3o, pode ser permitido ou n\u00E3o arestas ligarem um v\u00E9rtice a ele pr\u00F3prio e v\u00E9rtices e/ou arestas podem ter um peso (num\u00E9rico) associado. Se as arestas t\u00EAm uma dire\u00E7\u00E3o associada (indicada por uma seta na representa\u00E7\u00E3o gr\u00E1fica) temos um grafo direcionado, grafo orientado ou d\u00EDgrafo. Um grafo com um \u00FAnico v\u00E9rtice e sem arestas \u00E9 conhecido como o grafo trivial ou \"o ponto\". Estruturas que podem ser representadas por grafos est\u00E3o em toda parte e muitos problemas de interesse pr\u00E1tico podem ser formulados como quest\u00F5es sobre certos grafos. Por exemplo, a estrutura de links da Wikipedia pode ser representada por um d\u00EDgrafo: os v\u00E9rtices s\u00E3o os artigos da Wikipedia e existe uma aresta do artigo A para o artigo B se e somente se A cont\u00E9m um link para B. D\u00EDgrafos s\u00E3o tamb\u00E9m usados para representar m\u00E1quinas de estado finito. O desenvolvimento de algoritmos para manipular grafos \u00E9 um importante tema da ci\u00EAncia da computa\u00E7\u00E3o."@pt ,
"Teorie graf\u016F zkoum\u00E1 vlastnosti struktur, zvan\u00FDch grafy. Ty jsou tvo\u0159eny vrcholy, kter\u00E9 jsou vz\u00E1jemn\u011B spojen\u00E9 hranami. Zn\u00E1zor\u0148uje se obvykle jako mno\u017Eina bod\u016F spojen\u00FDch \u010Darami. Form\u00E1ln\u011B je graf uspo\u0159\u00E1danou dvojic\u00ED mno\u017Einy vrchol\u016F V a mno\u017Einy hran E: <math>G = \\left(V, E \\right)</math> Pomoc\u00ED graf\u016F lze reprezentovat struktury a \u00FAlohy z nejr\u016Fzn\u011Bj\u0161\u00EDch obor\u016F. Takt\u00E9\u017E mnoho probl\u00E9m\u016F praktick\u00E9ho \u017Eivota m\u016F\u017Ee b\u00FDt formulov\u00E1no jako \u00FAloha teorie graf\u016F - kup\u0159\u00EDkladu struktura vz\u00E1jemn\u00E9ho propojen\u00ED \u010Dl\u00E1nk\u016F Wikipedie. Jednotliv\u00E9 \u010Dl\u00E1nky jsou vrcholy grafu a odkaz z \u010Dl\u00E1nku A na \u010Dl\u00E1nek B je orientovanou hranou mezi vrcholy A a B. Struktura grafu m\u016F\u017Ee b\u00FDt roz\u0161\u00ED\u0159ena o ohodnocen\u00ED hran (tak\u00E9 ozna\u010Dov\u00E1no jako v\u00E1ha; m\u016F\u017Ee reprezentovat d\u00E9lku, n\u00E1klady na p\u0159esun, pr\u016Fchodnost apod. ) nebo vrcholu. V\u00FDsledkem je model re\u00E1ln\u00E9 s\u00EDt\u011B. Takov\u00E9 modely se pou\u017E\u00EDvaj\u00ED pro anal\u00FDzu dopravy nebo po\u010D\u00EDta\u010Dov\u00FDch s\u00EDt\u00ED (jako nap\u0159. internetu)."@cs ,
"In mathematics and computer science, graph theory is the study of graphs: mathematical structures used to model pairwise relations between objects from a certain collection. A \"graph\" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of vertices. A graph may be undirected, meaning that there is no distinction between the two vertices associated with each edge, or its edges may be directed from one vertex to another; see graph (mathematics) for more detailed definitions and for other variations in the types of graphs that are commonly considered. The graphs studied in graph theory should not be confused with \"graphs of functions\" and other kinds of graphs. Please refer to Glossary of graph theory for some basic definitions in graph theory."@en ,
"Graafiteoria eli Verkkoteoria tutkii graafien eli verkkojen ominaisuuksia."@fi ,
"Grafteori \u00E4r det omr\u00E5de inom matematiken som unders\u00F6ker egenskaper hos grafer. En graf \u00E4r en m\u00E4ngd punkter, kallade noder eller h\u00F6rn, sammanbundna med linjer, kallade b\u00E5gar eller kanter. Anledningen till att man valt orden noder och b\u00E5gar eller kanter och h\u00F6rn ist\u00E4llet f\u00F6r punkter och linjer \u00E4r att kanter och h\u00F6rn saknar de vanliga euklidiska egenskaperna f\u00F6r punkter och linjer. Man kan l\u00E4gga flera punkter p\u00E5 samma linje, men en kant kan bara g\u00E5 mellan max tv\u00E5 h\u00F6rn. Kanten kan dessutom g\u00E5 tillbaka till samma h\u00F6rn. Den kallas d\u00E5 loop. Antalet kant\u00E4ndar som ansluter till samma h\u00F6rn kallas h\u00F6rnets grad. Det \u00E4r m\u00F6jligt att flera kanter g\u00E5r mellan samma par av h\u00F6rn. Det kallas multipla kanter."@sv ,
"In termini informali, per grafo si intende una struttura costituita da: oggetti semplici, detti vertici (vertices) o nodi (nodes), collegamenti tra i vertici. I collegamenti possono essere: orientati, e in questo caso sono detti archi (arcs), e il grafo \u00E8 detto orientato non orientati, e in questo caso sono detti spigoli (edges), e il grafo \u00E8 detto non orientato eventualmente dati associati a nodi e/o collegamenti Per una definizione formale, vedi grafo. Un grafo viene generalmente raffigurato sul piano da punti o cerchietti, che rappresentano i nodi, e da segmenti o curve che collegano due nodi che rappresentano gli archi o gli spigoli. In questo caso, il posizionamento dei nodi e la forma degli archi o spigoli \u00E8 irrilevante, contano solo i nodi e le relazioni tra di loro. In altri termini, lo stesso grafo pu\u00F2 essere disegnato in molti modi diversi senza modificare le sue propriet\u00E0. Per un approfondimento sulla terminologia specifica della teoria dei grafi, si pu\u00F2 consultare il glossario di teoria dei grafi. Le strutture che possono essere rappresentate da grafi sono onnipresenti e molti problemi di interesse pratico possono essere formulati come questioni relative a grafi. In particolare, le reti possono essere descritte in forma di grafi. Ad esempio, la struttura dei link della Wikipedia, come tutti gli ipertesti, pu\u00F2 essere rappresentata da un grafo orientato, dove i vertici sono gli articoli e gli archi rappresentato l'esistenza di un link tra un articolo e l'altro. I grafi orientati sono anche utilizzati per rappresentare le macchine a stati finiti e molti altri formalismi, come ad esempio diagrammi di flusso, catene di Markov, schemi entit\u00E0-relazione, reti di Petri e molti altri. Lo sviluppo di algoritmi per maneggiare i grafi \u00E8 una delle aree di maggior interesse dell'informatica."@it ,
"De grafentheorie is een tak van wiskunde die de eigenschappen van grafen bestudeert. Een graaf bestaat uit een verzameling punten, knopen genoemd, waarvan sommige verbonden zijn door lijnen, de zijden, kanten of takken. Afhankelijk van de toepassing kunnen de lijnen gericht zijn, dan worden ze ook wel pijlen genoemd, men spreekt dan van een gerichte graaf (of digraaf). Ook worden wel gewichten aan de lijnen toegekend door middel van getallen, deze stellen dan bijvoorbeeld de afstand tussen twee punten voor. Een graaf met gewichten noemt men een gewogen graaf. Structuren die als grafen weergegeven kunnen worden zijn alomtegenwoordig, en veel praktische problemen kunnen als een probleem op een graaf gemodelleerd worden. Grafen worden bijvoorbeeld gebruikt om eindige toestandsmachines te modelleren of om een schematische routekaart te maken tussen een aantal plaatsen met de afstanden daartussen. Over deze grafen kunnen algoritmes uitgevoerd worden om bepaalde eigenschappen van zo'n graaf te berekenen; binnen de informatica is dit een redelijk belangrijk onderwerp. Complexe netwerken is een vrij recente stroming in het onderzoek rond grafen die minder focust op de studie van kleine grafen, en de eigenschappen van individuele knopen en bogen in deze grafen, maar eerder op de statistische eigenschappen van grootschalige netwerken."@nl ,
"En matem\u00E1ticas y en ciencias de la computaci\u00F3n, la teor\u00EDa de grafos (tambi\u00E9n llamada teor\u00EDa de las gr\u00E1ficas) estudia las propiedades de los grafos (tambi\u00E9n llamadas gr\u00E1ficas). Un grafo es un conjunto, no vac\u00EDo, de objetos llamados v\u00E9rtices (o nodos) y una selecci\u00F3n de pares de v\u00E9rtices, llamados aristas (edges en ingl\u00E9s) que pueden ser orientados o no. T\u00EDpicamente, un grafo se representa mediante una serie de puntos (los v\u00E9rtices) conectados por l\u00EDneas (las aristas)."@es ,
"\u0424\u0430\u0439\u043B:Graph. gif \u0413\u0440\u0430\u0444 \u0437\u0456 \u0448\u0456\u0441\u0442\u044C\u043C\u0430 \u0432\u0435\u0440\u0448\u0438\u043D\u0430\u043C\u0438 \u0442\u0430 \u0441\u0456\u043C\u043E\u043C\u0430 \u0440\u0435\u0431\u0440\u0430\u043C\u0438 \u0422\u0435\u043E\u0440\u0456\u044F \u0433\u0440\u0430\u0444\u0456\u0432 \u2014 \u0440\u043E\u0437\u0434\u0456\u043B \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438, \u0449\u043E \u0432\u0438\u0432\u0447\u0430\u0454 \u0432\u043B\u0430\u0441\u0442\u0438\u0432\u043E\u0441\u0442\u0456 \u0433\u0440\u0430\u0444\u0456\u0432. \u041E\u0441\u0442\u0430\u043D\u043D\u0456 \u0441\u043F\u0440\u043E\u0449\u0435\u043D\u043E \u043C\u043E\u0436\u043D\u0430 \u0440\u043E\u0437\u0433\u043B\u044F\u0434\u0430\u0442\u0438 \u044F\u043A \u0441\u0443\u043A\u0443\u043F\u043D\u0456\u0441\u0442\u044C \u0442\u043E\u0447\u043E\u043A \u0441\u043F\u043E\u043B\u0443\u0447\u0435\u043D\u0438\u0445 \u043B\u0456\u043D\u0456\u044F\u043C\u0438. \u0412\u0438\u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F \u0433\u0440\u0430\u0444\u0443 \u0454 \u043D\u0430\u0441\u0442\u0456\u043B\u044C\u043A\u0438 \u0437\u0430\u0433\u0430\u043B\u044C\u043D\u0438\u043C, \u0449\u043E \u0446\u0438\u043C \u0442\u0435\u0440\u043C\u0456\u043D\u043E\u043C \u043C\u043E\u0436\u043D\u0430 \u043E\u043F\u0438\u0441\u0443\u0432\u0430\u0442\u0438 \u0431\u0435\u0437\u043B\u0456\u0447 \u043F\u043E\u0434\u0456\u0439 \u0442\u0430 \u043E\u0431'\u0454\u043A\u0442\u0456\u0432 \u043F\u043E\u0432\u0441\u044F\u043A\u0434\u0435\u043D\u043D\u043E\u0433\u043E \u0436\u0438\u0442\u0442\u044F. \u0412\u0438\u0441\u043E\u043A\u0438\u0439 \u0440\u0456\u0432\u0435\u043D\u044C \u0430\u0431\u0441\u0442\u0440\u0430\u043A\u0446\u0456\u0457 \u0442\u0430 \u0443\u0437\u0430\u0433\u0430\u043B\u044C\u043D\u0435\u043D\u043D\u044F \u0434\u043E\u0437\u0432\u043E\u043B\u044F\u0454 \u0432\u0438\u043A\u043E\u0440\u0438\u0441\u0442\u043E\u0432\u0443\u0432\u0430\u0442\u0438 \u0442\u0438\u043F\u043E\u0432\u0456 \u0430\u043B\u0433\u043E\u0440\u0438\u0442\u043C\u0438 \u0442\u0435\u043E\u0440\u0456\u0457 \u0433\u0440\u0430\u0444\u0456\u0432 \u0434\u043B\u044F \u0432\u0438\u0440\u0456\u0448\u0435\u043D\u043D\u044F \u0437\u043E\u0432\u043D\u0456\u0448\u043D\u044C\u043E \u043D\u0435\u0441\u0445\u043E\u0436\u0438\u0445 \u0437\u0430\u0434\u0430\u0447 \u0443 \u0442\u0440\u0430\u043D\u0441\u043F\u043E\u0440\u0442\u043D\u0438\u0445 \u0456 \u043A\u043E\u043C\u043F'\u044E\u0442\u0435\u0440\u043D\u0438\u0445 \u043C\u0435\u0440\u0435\u0436\u0430\u0445, \u0431\u0443\u0434\u0456\u0432\u0435\u043B\u044C\u043D\u043E\u043C\u0443 \u043F\u0440\u043E\u0435\u043A\u0442\u0443\u0432\u0430\u043D\u043D\u0456, \u043C\u043E\u043B\u0435\u043A\u0443\u043B\u044F\u0440\u043D\u043E\u043C\u0443 \u043C\u043E\u0434\u0435\u043B\u044E\u0432\u0430\u043D\u043D\u0456 \u0442\u043E\u0449\u043E."@uk ,
"Grafteori er en gren i matematikk og informatikk der man studerer egenskapene til grafer. Grafer er matematiske strukturer som brukes til \u00E5 lage modeller for parvise relasjoner mellom objekter. I informatikken regnes graf som en abstrakt datastruktur, en teoretisk struktur som kan implementeres p\u00E5 ulike m\u00E5ter. Studier av algoritmer som behandler grafer er en viktig disiplin med mange praktiske anvendelser, i dag er dette i stor grad knyttet mot moderne datateknikk, men slike algoritmer var ogs\u00E5 utviklet f\u00F8r den digitale tidsalderen. Grafer og behandling av grafer er viktige verkt\u00F8y i mange hverdagslige problemstillinger som f. eks. ruteplanlegging, datanettverk og design av mikrobrikker. Opprinnelsen til grafteori ansees for \u00E5 v\u00E6re en artikkel publisert av Leonhard Euler i 1736, som tok for seg problemet Broene i K\u00F6nigsberg."@no ,
"\u56FE\u8BBA\uFF08graph theory\uFF09\u662F\u6570\u5B66\u7684\u4E00\u4E2A\u5206\u652F\uFF0C\u5B83\u4EE5\u56FE\uFF08graph\uFF09\u4E3A\u7814\u7A76\u5BF9\u8C61\uFF0C\u7814\u7A76\u9876\u70B9\uFF08vertex\uFF09\u548C\u8FB9\uFF08edge\uFF0C\u53C8\u79F0line\uFF09\u7EC4\u6210\u7684\u56FE\u5F62\u7684\u6570\u5B66\u7406\u8BBA\u548C\u65B9\u6CD5\u3002 \u56FE\u8BBA\u4E2D\u7684\u56FE\u662F\u7531\u82E5\u5E72\u7ED9\u5B9A\u7684\u9876\u70B9\u53CA\u8FDE\u63A5\u4E24\u9876\u70B9\u7684\u8FB9\u6240\u6784\u6210\u7684\u56FE\u5F62\uFF0C\u8FD9\u79CD\u56FE\u5F62\u901A\u5E38\u7528\u6765\u63CF\u8FF0\u67D0\u4E9B\u4E8B\u7269\u4E4B\u95F4\u7684\u67D0\u79CD\u7279\u5B9A\u5173\u7CFB\uFF0C\u7528\u9876\u70B9\u4EE3\u8868\u4E8B\u7269\uFF0C\u7528\u8FDE\u63A5\u4E24\u9876\u70B9\u7684\u8FB9\u8868\u793A\u76F8\u5E94\u4E24\u4E2A\u4E8B\u7269\u95F4\u5177\u6709\u8FD9\u79CD\u5173\u7CFB\u3002 \u56FE\u8BBA\u8D77\u6E90\u4E8E\u8457\u540D\u7684\u67EF\u5C3C\u65AF\u5821\u4E03\u6865\u95EE\u9898\u3002 \u56FE\u8BBA\u7684\u7814\u7A76\u5BF9\u8C61\u76F8\u5F53\u4E8E\u4E00\u7EF4\u7684\u62D3\u6251\u5B66\u3002"@zh ,
"F\u00E1jl:6n-graf. svg Gr\u00E1f. A gr\u00E1felm\u00E9let a matematika, ezen bel\u00FCl a kombinatorika egyik fontos \u00E1ga. Kialak\u00EDt\u00E1s\u00E1hoz jelent\u0151s m\u00E9rt\u00E9kben hozz\u00E1j\u00E1rultak a magyar kombinatorikai iskola tagjai: K\u0151nig D\u00E9nes, Erd\u0151s P\u00E1l, Gallai Tibor, R\u00E9nyi Alfr\u00E9d, Lov\u00E1sz L\u00E1szl\u00F3, P\u00F3sa Lajos."@hu ,
"\u0424\u0430\u0439\u043B:6n-graf. svg \u0433\u0440\u0430\u0444 \u0441 \u0448\u0435\u0441\u0442\u044C\u044E \u0432\u0435\u0440\u0448\u0438\u043D\u0430\u043C\u0438 \u0438 \u0441\u0435\u043C\u044C\u044E \u0440\u0451\u0431\u0440\u0430\u043C\u0438 \u0422\u0435\u043E\u0301\u0440\u0438\u044F \u0433\u0440\u0430\u0301\u0444\u043E\u0432 \u2014 \u0440\u0430\u0437\u0434\u0435\u043B \u0434\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u043E\u0439 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438, \u0438\u0437\u0443\u0447\u0430\u044E\u0449\u0438\u0439 \u0441\u0432\u043E\u0439\u0441\u0442\u0432\u0430 \u0433\u0440\u0430\u0444\u043E\u0432. \u0412 \u043E\u0431\u0449\u0435\u043C \u0441\u043C\u044B\u0441\u043B\u0435 \u0433\u0440\u0430\u0444 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043A\u0430\u043A \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E \u0432\u0435\u0440\u0448\u0438\u043D (\u0443\u0437\u043B\u043E\u0432), \u0441\u043E\u0435\u0434\u0438\u043D\u0451\u043D\u043D\u044B\u0445 \u0440\u0451\u0431\u0440\u0430\u043C\u0438. \u0412 \u0441\u0442\u0440\u043E\u0433\u043E\u043C \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u0438 \u0433\u0440\u0430\u0444\u043E\u043C \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u0442\u0430\u043A\u0430\u044F \u043F\u0430\u0440\u0430 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432 G={R,V}, \u0433\u0434\u0435 V \u0435\u0441\u0442\u044C \u043F\u043E\u0434\u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E \u043B\u044E\u0431\u043E\u0433\u043E \u0441\u0447\u0451\u0442\u043D\u043E\u0433\u043E \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430, \u0430 R \u2014 \u043F\u043E\u0434\u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E V\u00D7V. \u0422\u0435\u043E\u0440\u0438\u044F \u0433\u0440\u0430\u0444\u043E\u0432 \u043D\u0430\u0445\u043E\u0434\u0438\u0442 \u043F\u0440\u0438\u043C\u0435\u043D\u0435\u043D\u0438\u0435, \u043D\u0430\u043F\u0440\u0438\u043C\u0435\u0440, \u0432 \u0433\u0435\u043E\u0438\u043D\u0444\u043E\u0440\u043C\u0430\u0446\u0438\u043E\u043D\u043D\u044B\u0445 \u0441\u0438\u0441\u0442\u0435\u043C\u0430\u0445 (\u0413\u0418\u0421). \u0421\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044E\u0449\u0438\u0435 \u0438\u043B\u0438 \u0432\u043D\u043E\u0432\u044C \u043F\u0440\u043E\u0435\u043A\u0442\u0438\u0440\u0443\u0435\u043C\u044B\u0435 \u0434\u043E\u043C\u0430, \u0441\u043E\u043E\u0440\u0443\u0436\u0435\u043D\u0438\u044F, \u043A\u0432\u0430\u0440\u0442\u0430\u043B\u044B \u0438 \u0442. \u043F. \u0440\u0430\u0441\u0441\u043C\u0430\u0442\u0440\u0438\u0432\u0430\u044E\u0442\u0441\u044F \u043A\u0430\u043A \u0432\u0435\u0440\u0448\u0438\u043D\u044B, \u0430 \u0441\u043E\u0435\u0434\u0438\u043D\u044F\u044E\u0449\u0438\u0435 \u0438\u0445 \u0434\u043E\u0440\u043E\u0433\u0438, \u0438\u043D\u0436\u0435\u043D\u0435\u0440\u043D\u044B\u0435 \u0441\u0435\u0442\u0438, \u043B\u0438\u043D\u0438\u0438 \u044D\u043B\u0435\u043A\u0442\u0440\u043E\u043F\u0435\u0440\u0435\u0434\u0430\u0447\u0438 \u0438 \u0442. \u043F. \u2014 \u043A\u0430\u043A \u0440\u0451\u0431\u0440\u0430. \u041F\u0440\u0438\u043C\u0435\u043D\u0435\u043D\u0438\u0435 \u0440\u0430\u0437\u043B\u0438\u0447\u043D\u044B\u0445 \u0432\u044B\u0447\u0438\u0441\u043B\u0435\u043D\u0438\u0439, \u043F\u0440\u043E\u0438\u0437\u0432\u043E\u0434\u0438\u043C\u044B\u0445 \u043D\u0430 \u0442\u0430\u043A\u043E\u043C \u0433\u0440\u0430\u0444\u0435, \u043F\u043E\u0437\u0432\u043E\u043B\u044F\u0435\u0442, \u043D\u0430\u043F\u0440\u0438\u043C\u0435\u0440, \u043D\u0430\u0439\u0442\u0438 \u043A\u0440\u0430\u0442\u0447\u0430\u0439\u0448\u0438\u0439 \u043E\u0431\u044A\u0435\u0437\u0434\u043D\u043E\u0439 \u043F\u0443\u0442\u044C \u0438\u043B\u0438 \u0431\u043B\u0438\u0436\u0430\u0439\u0448\u0438\u0439 \u043F\u0440\u043E\u0434\u0443\u043A\u0442\u043E\u0432\u044B\u0439 \u043C\u0430\u0433\u0430\u0437\u0438\u043D, \u0441\u043F\u043B\u0430\u043D\u0438\u0440\u043E\u0432\u0430\u0442\u044C \u043E\u043F\u0442\u0438\u043C\u0430\u043B\u044C\u043D\u044B\u0439 \u043C\u0430\u0440\u0448\u0440\u0443\u0442. \u0422\u0435\u043E\u0440\u0438\u044F \u0433\u0440\u0430\u0444\u043E\u0432 \u0441\u043E\u0434\u0435\u0440\u0436\u0438\u0442 \u0431\u043E\u043B\u044C\u0448\u043E\u0435 \u043A\u043E\u043B\u0438\u0447\u0435\u0441\u0442\u0432\u043E \u043D\u0435\u0440\u0435\u0448\u0451\u043D\u043D\u044B\u0445 \u043F\u0440\u043E\u0431\u043B\u0435\u043C \u0438 \u043F\u043E\u043A\u0430 \u043D\u0435\u0434\u043E\u043A\u0430\u0437\u0430\u043D\u043D\u044B\u0445 \u0433\u0438\u043F\u043E\u0442\u0435\u0437."@ru ,
"La teoria de grafs \u00E9s una branca de les matem\u00E0tiques i la inform\u00E0tica que es dedica a l'estudi dels grafs i les seves propietats. En aquest context, un graf consisteix en una col\u00B7lecci\u00F3 de v\u00E8rtexs (o nodes) conectats per l\u00EDnies anomenades arestes. Els grafs es representen gr\u00E0ficament amb un punt per cada v\u00E8rtex, i tra\u00E7ant una l\u00EDnea entre els v\u00E8rtexs conectats. Si el graf t\u00E9 direcci\u00F3, aquesta se simbolitza amb una fletxa. Les aplicacions de la teoria de grafs giren al voltant d'estructures que poden ser sistematitzades amb grafs com per exemple l'estructura de llocs web, an\u00E0lisi de xarxes, estudi de mol\u00E8cules en qu\u00EDmica i f\u00EDsica, o en altres camps com els estudis sociol\u00F2gics. El precursor de la teoria de grafs fou Leonhard Euler, que la va iniciar tot intentant resoldre el problema dels set ponts de K\u00F6nigsberg."@ca ;
rdfs:comment "In mathematics and computer science, graph theory is the study of graphs: mathematical structures used to model pairwise relations between objects from a certain collection. A \"graph\" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of vertices."@en ,
"Grafteori \u00E4r det omr\u00E5de inom matematiken som unders\u00F6ker egenskaper hos grafer. En graf \u00E4r en m\u00E4ngd punkter, kallade noder eller h\u00F6rn, sammanbundna med linjer, kallade b\u00E5gar eller kanter. Anledningen till att man valt orden noder och b\u00E5gar eller kanter och h\u00F6rn ist\u00E4llet f\u00F6r punkter och linjer \u00E4r att kanter och h\u00F6rn saknar de vanliga euklidiska egenskaperna f\u00F6r punkter och linjer. Man kan l\u00E4gga flera punkter p\u00E5 samma linje, men en kant kan bara g\u00E5 mellan max tv\u00E5 h\u00F6rn."@sv ,
"\u00C7izge kuram\u0131, \u00E7izgeleri yani graflar\u0131 inceleyen matematik dal\u0131d\u0131r. \u00C7izge u\u00E7lar ve bu u\u00E7lar\u0131 birbirine ba\u011Flayan kenarlardan olu\u015Fan bir t\u00FCr a\u011F yap\u0131s\u0131d\u0131r."@tr ,
"F\u00E1jl:6n-graf. svg Gr\u00E1f. A gr\u00E1felm\u00E9let a matematika, ezen bel\u00FCl a kombinatorika egyik fontos \u00E1ga. Kialak\u00EDt\u00E1s\u00E1hoz jelent\u0151s m\u00E9rt\u00E9kben hozz\u00E1j\u00E1rultak a magyar kombinatorikai iskola tagjai: K\u0151nig D\u00E9nes, Erd\u0151s P\u00E1l, Gallai Tibor, R\u00E9nyi Alfr\u00E9d, Lov\u00E1sz L\u00E1szl\u00F3, P\u00F3sa Lajos."@hu ,
"La teoria de grafs \u00E9s una branca de les matem\u00E0tiques i la inform\u00E0tica que es dedica a l'estudi dels grafs i les seves propietats. En aquest context, un graf consisteix en una col\u00B7lecci\u00F3 de v\u00E8rtexs (o nodes) conectats per l\u00EDnies anomenades arestes. Els grafs es representen gr\u00E0ficament amb un punt per cada v\u00E8rtex, i tra\u00E7ant una l\u00EDnea entre els v\u00E8rtexs conectats. Si el graf t\u00E9 direcci\u00F3, aquesta se simbolitza amb una fletxa."@ca ,
"Die Graphentheorie ist ein Teilgebiet der Mathematik, das die Eigenschaften von Graphen und ihre Beziehungen zueinander untersucht. Dadurch, dass einerseits viele algorithmische Probleme auf Graphen zur\u00FCckgef\u00FChrt werden k\u00F6nnen und andererseits die L\u00F6sung graphentheoretischer Probleme oft auf Algorithmen basiert, ist die Graphentheorie auch in der Informatik, insbesondere der Komplexit\u00E4tstheorie, von gro\u00DFer Bedeutung. Die Untersuchung von Graphen ist auch Inhalt der Netzwerktheorie."@de ,
"Teorie graf\u016F zkoum\u00E1 vlastnosti struktur, zvan\u00FDch grafy. Ty jsou tvo\u0159eny vrcholy, kter\u00E9 jsou vz\u00E1jemn\u011B spojen\u00E9 hranami. Zn\u00E1zor\u0148uje se obvykle jako mno\u017Eina bod\u016F spojen\u00FDch \u010Darami. Form\u00E1ln\u011B je graf uspo\u0159\u00E1danou dvojic\u00ED mno\u017Einy vrchol\u016F V a mno\u017Einy hran E: <math>G = \\left(V, E \\right)</math> Pomoc\u00ED graf\u016F lze reprezentovat struktury a \u00FAlohy z nejr\u016Fzn\u011Bj\u0161\u00EDch obor\u016F."@cs ,
"\u0424\u0430\u0439\u043B:Graph. gif \u0413\u0440\u0430\u0444 \u0437\u0456 \u0448\u0456\u0441\u0442\u044C\u043C\u0430 \u0432\u0435\u0440\u0448\u0438\u043D\u0430\u043C\u0438 \u0442\u0430 \u0441\u0456\u043C\u043E\u043C\u0430 \u0440\u0435\u0431\u0440\u0430\u043C\u0438 \u0422\u0435\u043E\u0440\u0456\u044F \u0433\u0440\u0430\u0444\u0456\u0432 \u2014 \u0440\u043E\u0437\u0434\u0456\u043B \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438, \u0449\u043E \u0432\u0438\u0432\u0447\u0430\u0454 \u0432\u043B\u0430\u0441\u0442\u0438\u0432\u043E\u0441\u0442\u0456 \u0433\u0440\u0430\u0444\u0456\u0432. \u041E\u0441\u0442\u0430\u043D\u043D\u0456 \u0441\u043F\u0440\u043E\u0449\u0435\u043D\u043E \u043C\u043E\u0436\u043D\u0430 \u0440\u043E\u0437\u0433\u043B\u044F\u0434\u0430\u0442\u0438 \u044F\u043A \u0441\u0443\u043A\u0443\u043F\u043D\u0456\u0441\u0442\u044C \u0442\u043E\u0447\u043E\u043A \u0441\u043F\u043E\u043B\u0443\u0447\u0435\u043D\u0438\u0445 \u043B\u0456\u043D\u0456\u044F\u043C\u0438."@uk ,
"A Teoria dos Grafos \u00E9 um ramo da matem\u00E1tica que estuda as rela\u00E7\u00F5es entre os objetos de um determinado conjunto. Grafo \u00E9 uma estrutura G(V,A) onde V \u00E9 um conjunto n\u00E3o vazio de objetos denominados v\u00E9rtices e A \u00E9 um conjunto de pares n\u00E3o ordenados de V, chamado arestas. Dependendo da aplica\u00E7\u00E3o, arestas podem ou n\u00E3o ter dire\u00E7\u00E3o, pode ser permitido ou n\u00E3o arestas ligarem um v\u00E9rtice a ele pr\u00F3prio e v\u00E9rtices e/ou arestas podem ter um peso (num\u00E9rico) associado."@pt ,
"Grafteori er en gren i matematikk og informatikk der man studerer egenskapene til grafer. Grafer er matematiske strukturer som brukes til \u00E5 lage modeller for parvise relasjoner mellom objekter. I informatikken regnes graf som en abstrakt datastruktur, en teoretisk struktur som kan implementeres p\u00E5 ulike m\u00E5ter."@no ,
"Teoria graf\u00F3w to dzia\u0142 matematyki zajmuj\u0105cy si\u0119 badaniem w\u0142asno\u015Bci graf\u00F3w. Rozwijanie algorytm\u00F3w wyznaczaj\u0105cych pewne w\u0142a\u015Bciwo\u015Bci graf\u00F3w jest jednym z bardziej znacz\u0105cych p\u00F3l dzia\u0142ania informatyki. Algorytmy te stosuje si\u0119 do rozwi\u0105zywania wielu zada\u0144 praktycznych, cz\u0119sto w dziedzinach na poz\u00F3r nie zwi\u0105zanych z grafami."@pl ,
"Graafiteoria eli Verkkoteoria tutkii graafien eli verkkojen ominaisuuksia."@fi ,
"En matem\u00E1ticas y en ciencias de la computaci\u00F3n, la teor\u00EDa de grafos (tambi\u00E9n llamada teor\u00EDa de las gr\u00E1ficas) estudia las propiedades de los grafos (tambi\u00E9n llamadas gr\u00E1ficas). Un grafo es un conjunto, no vac\u00EDo, de objetos llamados v\u00E9rtices (o nodos) y una selecci\u00F3n de pares de v\u00E9rtices, llamados aristas (edges en ingl\u00E9s) que pueden ser orientados o no. T\u00EDpicamente, un grafo se representa mediante una serie de puntos (los v\u00E9rtices) conectados por l\u00EDneas (las aristas)."@es ,
"La th\u00E9orie des graphes est une branche commune \u00E0 l'informatique et aux math\u00E9matiques \u00E9tudiant les graphes et les objets qui lui sont propres, comme par exemple les chemins. Le concept de graphe, \u00E0 ne pas confondre avec le graphe d'une fonction, permet d'\u00E9tudier les propri\u00E9t\u00E9s de certaines structures comme les r\u00E9seaux ou, plus largement, les relations binaires. Les algorithmes de la th\u00E9orie des graphes ont ainsi de nombreuses applications importantes."@fr ,
"In termini informali, per grafo si intende una struttura costituita da: oggetti semplici, detti vertici (vertices) o nodi (nodes), collegamenti tra i vertici. I collegamenti possono essere: orientati, e in questo caso sono detti archi (arcs), e il grafo \u00E8 detto orientato non orientati, e in questo caso sono detti spigoli (edges), e il grafo \u00E8 detto non orientato eventualmente dati associati a nodi e/o collegamenti Per una definizione formale, vedi grafo."@it ,
"\u0424\u0430\u0439\u043B:6n-graf. svg \u0433\u0440\u0430\u0444 \u0441 \u0448\u0435\u0441\u0442\u044C\u044E \u0432\u0435\u0440\u0448\u0438\u043D\u0430\u043C\u0438 \u0438 \u0441\u0435\u043C\u044C\u044E \u0440\u0451\u0431\u0440\u0430\u043C\u0438 \u0422\u0435\u043E\u0301\u0440\u0438\u044F \u0433\u0440\u0430\u0301\u0444\u043E\u0432 \u2014 \u0440\u0430\u0437\u0434\u0435\u043B \u0434\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u043E\u0439 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438, \u0438\u0437\u0443\u0447\u0430\u044E\u0449\u0438\u0439 \u0441\u0432\u043E\u0439\u0441\u0442\u0432\u0430 \u0433\u0440\u0430\u0444\u043E\u0432. \u0412 \u043E\u0431\u0449\u0435\u043C \u0441\u043C\u044B\u0441\u043B\u0435 \u0433\u0440\u0430\u0444 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043A\u0430\u043A \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E \u0432\u0435\u0440\u0448\u0438\u043D (\u0443\u0437\u043B\u043E\u0432), \u0441\u043E\u0435\u0434\u0438\u043D\u0451\u043D\u043D\u044B\u0445 \u0440\u0451\u0431\u0440\u0430\u043C\u0438."@ru ,
"\u30B0\u30E9\u30D5\u7406\u8AD6\uFF08\u30B0\u30E9\u30D5\u308A\u308D\u3093\u3001Graph theory\uFF09\u306F\u3001\u6570\u5B66\u306E\u4E00\u5206\u91CE\u3002\u30CE\u30FC\u30C9\uFF08\u7BC0\u70B9\u30FB\u9802\u70B9\u3001\u82F1\u8A9E\uFF1Anode\uFF09\u306E\u96C6\u5408\u3068\u30A8\u30C3\u30B8\uFF08\u679D\u30FB\u8FBA\u3001\u82F1\u8A9E\uFF1Aedge\uFF09\u306E\u96C6\u5408\u3067\u69CB\u6210\u3055\u308C\u308B\u30B0\u30E9\u30D5\u306E\u6027\u8CEA\u306B\u3064\u3044\u3066\u7814\u7A76\u3059\u308B\u5B66\u554F\u3067\u3042\u308B\u3002\u306A\u304A\u300C\u30A8\u30C3\u30B8\u300D\u3092\u30EA\u30F3\u30AF\uFF08\u82F1\u8A9E\uFF1Alink\uFF09\u3068\u3044\u3046\u5834\u5408\u3082\u3042\u308B\u3002 \u30B3\u30F3\u30D4\u30E5\u30FC\u30BF\u306E\u30C7\u30FC\u30BF\u69CB\u9020\u3001\u30A2\u30EB\u30B4\u30EA\u30BA\u30E0\u306A\u3069\u306B\u5E83\u304F\u5FDC\u7528\u3055\u308C\u3066\u3044\u308B\u3002"@ja ,
""@zh ,
"De grafentheorie is een tak van wiskunde die de eigenschappen van grafen bestudeert. Een graaf bestaat uit een verzameling punten, knopen genoemd, waarvan sommige verbonden zijn door lijnen, de zijden, kanten of takken. Afhankelijk van de toepassing kunnen de lijnen gericht zijn, dan worden ze ook wel pijlen genoemd, men spreekt dan van een gerichte graaf (of digraaf)."@nl ;
foaf:depiction .
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