Lower bounds for Ramsey numbers as a statistical physics problem
Combinatorics
2022-04-01 v2 Statistical Mechanics
Abstract
Ramsey's theorem, concerning the guarantee of certain monochromatic patterns in large enough edge-coloured complete graphs, is a fundamental result in combinatorial mathematics. In this work, we highlight the connection between this abstract setting and a statistical physics problem. Specifically, we design a classical Hamiltonian that favours configurations in a way to establish lower bounds on Ramsey numbers. As a proof of principle we then use Monte Carlo methods to obtain such lower bounds, finding rough agreement with known literature values in a few cases we investigated. We discuss numerical limitations of our approach and indicate a path towards the treatment of larger graph sizes.
Cite
@article{arxiv.2112.11426,
title = {Lower bounds for Ramsey numbers as a statistical physics problem},
author = {Jurriaan Wouters and Aris Giotis and Ross Kang and Dirk Schuricht and Lars Fritz},
journal= {arXiv preprint arXiv:2112.11426},
year = {2022}
}