非齐次随机图的团与色数
Cliques and Chromatic Number in Inhomogenous Random Graphs
摘要：
本文研究了边概率可以任意小的非齐次随机图的团和色数。我们使用递归的方法来获得一个温和的正平均边密度假设下的最大团大小的估计。作为推论，对于边概率$p_n$满足$\frac{1}{n^{α_1}} \leq p_n \leq 1-\frac{1}{n^{α_2}}$的所有取值范围，对于某些正的常数$α_1$和$α_2$，我们也得到了齐次随机图的最大团大小和色数的一致界.
英文摘要：
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 $\frac{1}{n^{α_1}} \leq p_n \leq 1-\frac{1}{n^{α_2}}$ for some positive constants $α_1$ and $α_2$.
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