On the Chromatic Number in the Stochastic Block Model

Electronic Journal of Combinatorics

article

Mikhail Isaev¹  Mihyun Kang² 

[1] School of Mathematics Monash University 3800 Clayton;Graz University of Technology

DOI  :  10.37236/10728

学科分类：统计和概率

来源: Electronic Journal Of Combinatorics

【 摘 要 】

We prove a generalisation of Bollobás' classical result on the asymptotics of the chromatic number of the binomial random graph to the stochastic block model. In addition, by allowing the number of blocks to grow, we determine the chromatic number in the Chung-Lu model. Our approach is based on the estimates for the weighted independence number, where weights are specifically designed to encapsulate inhomogeneities of the random graph.

【 授权许可】

CC BY