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The upper bound on number of graphs, with fixed number of vertices, that vertices can be colored with n colors

Kamil Kulesza·Zbigniew Kotulski
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Abstract

In the paper we state and prove theorem describing the upper bound on number of the graphs that have fixed number of vertices |V| and can be colored with the fixed number of n colors. The bound relates both numbers using power of 2, while the exponent is the difference between |V| and n. We also state three conjectures on the number of graphs that have fixed number of vertices |V| and chromatic number n.

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Kamil Kulesza, Zbigniew Kotulski. 2003-11-25. The upper bound on number of graphs, with fixed number of vertices, that vertices can be colored with n colors. https://arxiv.org/abs/math/0310485

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