About: 2-factor theorem

In the mathematical discipline of graph theory, the 2-factor theorem, discovered by Julius Petersen, is one of the earliest works in graph theory. It can be stated as follows: 2-factor theorem. Let G be a regular graph whose degree is an even number, 2k. Then the edges of G can be partitioned into k edge-disjoint 2-factors. Here, a 2-factor is a subgraph of G in which all vertices have degree two; that is, it is a collection of cycles that together touch each vertex exactly once.