About: Rainbow-independent set

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In graph theory, a rainbow-independent set (ISR) is an independent set in a graph, in which each vertex has a different color. Formally, let G = (V, E) be a graph, and suppose vertex set V is partitioned into m subsets V1, …, Vm, called "colors". A set U of vertices is called a rainbow-independent set if it satisfies both the following conditions: * It is an independent set – every two vertices in U are not adjacent (there is no edge between them); * It is a rainbow set – U contains at most a single vertex from each color Vi.

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  • In graph theory, a rainbow-independent set (ISR) is an independent set in a graph, in which each vertex has a different color. Formally, let G = (V, E) be a graph, and suppose vertex set V is partitioned into m subsets V1, …, Vm, called "colors". A set U of vertices is called a rainbow-independent set if it satisfies both the following conditions: * It is an independent set – every two vertices in U are not adjacent (there is no edge between them); * It is a rainbow set – U contains at most a single vertex from each color Vi. Other terms used in the literature are independent set of representatives, independent transversal, and independent system of representatives. As an example application, consider a faculty with m departments, where some faculty members dislike each other. The dean wants to construct a committee with m members, one member per department, but without any pair of members who dislike each other. This problem can be presented as finding an ISR in a graph in which the nodes are the faculty members, the edges describe the "dislike" relations, and the subsets V1, …, Vm are the departments. (en)
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  • In graph theory, a rainbow-independent set (ISR) is an independent set in a graph, in which each vertex has a different color. Formally, let G = (V, E) be a graph, and suppose vertex set V is partitioned into m subsets V1, …, Vm, called "colors". A set U of vertices is called a rainbow-independent set if it satisfies both the following conditions: * It is an independent set – every two vertices in U are not adjacent (there is no edge between them); * It is a rainbow set – U contains at most a single vertex from each color Vi. (en)
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  • Rainbow-independent set (en)
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