My Math Forum digraph: cycle of an even length and coloring the vertices
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 April 13th, 2010, 05:45 AM #1 Newbie   Joined: Apr 2010 Posts: 1 Thanks: 0 digraph: cycle of an even length and coloring the vertices Prove that the following two conditions for a strongly connected directed graph G are equivalent: 1. G contains a directed cycle of an even length. 2. The vertices of G can be colored by 2 colors (each vertex receives one color) in such a way that for each vertex u there exists a directed edge (u, v) with v having the color different from the color of u.

 Tags coloring, cycle, digraph, length, vertices

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