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

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

2003-10-31

arxiv.org/abs/math/0310485v2

Mathematics

Combinatorics

7 pages, submitted for journal publication

Scientific paper

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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