Gaussian random graphs and Ramsey numbers
Zach Hunter, Aleksa Milojevi\'c, Benny Sudakov
TL;DR
This paper introduces a new approach using Gaussian random graphs to improve lower bounds on Ramsey numbers, simplifying analysis and achieving better quantitative results.
Contribution
It provides a simplified proof and improved bounds for Ramsey numbers using Gaussian random graphs, building on recent advances.
Findings
Exponential improvement in Ramsey lower bounds
Simplified analysis via Gaussian random graphs
Enhanced quantitative bounds on Ramsey numbers
Abstract
We give a simple proof of the recent remarkable exponential improvement for Ramsey lower bounds, obtained by Ma, Shen and Xie. Our key ingredient is an alternative construction based on Gaussian random graphs, which allows us to simplify their analysis significantly. As a consequence of this simpler analysis, we also obtain better quantitative bounds.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Markov Chains and Monte Carlo Methods · Computability, Logic, AI Algorithms