On the Chromatic Number of Non-Sparse Random Intersection Graphs

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• 作者：Sotiris E. Nikoletseas ; Christoforos L. Raptopoulos&#8230
• 关键词：Random intersection graphs ; Proper coloring ; Martingales ; Probabilistic method
• 刊名：Theory of Computing Systems
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：60
• 期：1
• 页码：112-127
• 全文大小：
• 刊物类别：Computer Science
• 刊物主题：Theory of Computation; Computational Mathematics and Numerical Analysis;
• 出版者：Springer US
• ISSN：1433-0490
• 卷排序：60

文摘

An intersection graph of n vertices assumes that each vertex is equipped with a subset of a global label set. Two vertices share an edge when their label sets intersect. Random intersection graphs (RIGs) (as defined in Karoński et al. Comb. Probab. Comput. J. 8, 131–159 (1999); Singer-Cohen (1995)) consider label sets formed by the following experiment: each vertex, independently and uniformly, examines all the labels (m in total) one by one. Each examination is independent and the vertex succeeds to put the label in her set with probability p. Such graphs can capture interactions in networks due to sharing of resources among nodes. In this paper, we discuss various structural and algorithmic results concerning random intersection graphs and we focus on the computational problem of properly coloring random instances of the binomial random intersection graphs model. For the latter, we consider a range of parameters m, p for which RIGs differ substantially from Erdős-Rényi random graphs and for which greedy approaches fail.