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Melnikov, L. S.


Graph Theory » Coloring » Vertex coloring

Melnikov's valency-variety problem ★

Author(s): Melnikov

Problem   The valency-variety $ w(G) $ of a graph $ G $ is the number of different degrees in $ G $. Is the chromatic number of any graph $ G $ with at least two vertices greater than $$\ceil{ \frac{\floor{w(G)/2}}{|V(G)| - w(G)} } ~ ?$$

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Posted by asp
updated March 3rd, 2013
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