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An improved method for recursively computing upper bounds for two-colour\n Ramsey numbers

2018/04/01 by Oliver Krüger, Krüger, Oliver
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1804.00322

openalex publication_date 2018/04/01 · openalex created_date 2019/11/22 · openalex updated_date 2026/07/28

Abstract

The two-colour Ramsey number R(m,n) is the least natural number p such\nthat any graph of order p must contain either a clique of size m or an\nindependent set of size n. We exhibit a method for computing upper bounds for\nR(m,n) recursively, using known upper bounds of R(\⋅,\⋅) with lower\nvalues for at least one of the arguments. We also give an example of how this\nmethod could be used to improve several of the best known bounds that are\navailable in the literature (which however soon will be obsolete due to a\nforthcoming work).\n

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