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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

Published 2003-10-31, updated 2003-11-25Version 2

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.

Comments: 7 pages, submitted for journal publication
Categories: math.CO
Subjects: 05C15, 05C30
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