Independent sets in random graphs from the weighted second moment method
Varsha Dani, Cristopher Moore
TL;DR
This paper introduces a weighted second moment method to establish new lower bounds on the size of maximum independent sets in random graphs with specified average degree, advancing understanding of graph independence properties.
Contribution
It develops a novel weighted second moment technique to improve bounds on independent set sizes in random graphs, a significant methodological advancement.
Findings
New lower bounds on maximum independent set size
Weighted second moment method proves more effective
Method applicable to graphs with given average degree
Abstract
We prove new lower bounds on the likely size of a maximum independent set in a random graph with a given average degree. Our method is a weighted version of the second moment method, where we give each independent set a weight based on the total degree of its vertices.
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