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arXiv · 1210.0412

The rate of growth of the minimum clique size of graphs of given order and chromatic number

Csaba Biró·Kris Wease
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Abstract

Let $Q(n,c)$ denote the minimum clique number over graphs with $n$ vertices and chromatic number $c$. We determine the rate of growth of of the sequence ${Q(n,\lceil rn \rceil)}_{n=1}^\infty$ for any fixed $0<r\leq 1$. We also give a better upper bound for $Q(n,\lceil rn \rceil)$.

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Csaba Biró, Kris Wease. 2014-02-03. The rate of growth of the minimum clique size of graphs of given order and chromatic number. https://arxiv.org/abs/1210.0412

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