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arXiv · 1704.04591

Cliques and Chromatic Number in Inhomogenous Random Graphs

Ghurumuruhan Ganesan
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Abstract

In this paper, we study cliques and chromatic number of inhomogenous random graphs where the individual edge probabilities could be arbitrarily low. We use a recursive method to obtain estimates on the maximum clique size under a mild positive average edge density assumption. As a Corollary, we also obtain uniform bounds on the maximum clique size and chromatic number for homogenous random graphs for all ranges of the edge probability $p_n$ satisfying $\frac{1}{n^{\alpha_1}} \leq p_n \leq 1-\frac{1}{n^{\alpha_2}}$ for some positive constants $\alpha_1$ and $\alpha_2$.

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Ghurumuruhan Ganesan. 2017-04-15. Cliques and Chromatic Number in Inhomogenous Random Graphs. https://arxiv.org/abs/1704.04591

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