Moment Calculus on Ramsey Graph

TL;DR

This paper explores the application of moment calculus to Ramsey theory, specifically relating Ramsey numbers to the distribution of monochromatic subgraphs in random graphs, and reviews the Delaporte distribution's role in this context.

Contribution

It introduces a novel approach connecting moment calculus with Ramsey numbers and reviews the connection with the Delaporte distribution in this setting.

Findings

Relation between Ramsey numbers and moment calculus established

Distribution of monochromatic subgraphs analyzed in random graphs

Connection with Delaporte distribution reviewed

Abstract

When I did my thesis defense presentation eleven years ago, I chose to present the subject of Ramsey theory from the moment calculus perspective. I don't think I did too well there (although I passed). Time has passed and this is the chance to redeem myself. Here we relate Ramsey numbers, $R(k,k)$, with the method of moment calculus by checking the distribution of numbers of monochromatic complete subgraph of $k$ vertices in the random graphs. We also review Delaporte distribution's connection that was mentioned in the paper by Robertson, Cipolli and Dascalu.