A lower bound on the hypergraph Ramsey number R(4,5;3)

2016/07/27 by Janusz Dybizbański · 1 citation
Mathematics · Computer Science · #Limits and Structures in Graph Theory #Advanced Topology and Set Theory #Advanced Graph Theory Research #Hypergraph #Ramsey's theorem #Combinatorics #Mathematics #Set (abstract data type) #Element (criminal law) #Upper and lower bounds #Discrete mathematics #Graph #Computer science

paper · doi:10.11575/cdm.v13i2.62416

openalex publication_date 2016/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The finite version of Ramsey's theorem says that for positive integers r, k, a₁,... ,a_r, there exists a least number n=R(a₁, …, a_r; k) so that if X is an n-element set and all k-subsets of X are r-coloured, then there exists an i and an a_i-set A so that all k-subsets of A are coloured with the ith colour. In this paper, the bound R(4, 5; 3) >= 35 is shown by using a SAT solver to construct a red--blue colouring of the triples chosen from a 34-element set.

Cited by

• Ramsey's theorem [wikipedia]

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• A survey of hypergraph Ramsey problems
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