The hard-core model in graph theory
Combinatorics
2025-09-04 v2 Discrete Mathematics
Probability
Abstract
An independent set may not contain both a vertex and one of its neighbours. This basic fact makes the uniform distribution over independent sets rather special. We consider the hard-core model, an essential generalization of the uniform distribution over independent sets. We show how its local analysis yields remarkable insights into the global structure of independent sets in the host graph, in connection with, for instance, Ramsey numbers, graph colourings, and sphere packings.
Cite
@article{arxiv.2501.03379,
title = {The hard-core model in graph theory},
author = {Ewan Davies and Ross J. Kang},
journal= {arXiv preprint arXiv:2501.03379},
year = {2025}
}
Comments
35 pages; prepared as a chapter for a forthcoming volume, Topics in Probabilistic Graph Theory; v2 refers to some selected newer developments