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April 13th, 2010, 05:45 AM   #1
ry.
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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.
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coloring, cycle, digraph, length, vertices



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