New Lower Bounds for 28 Classical Ramsey Numbers

2015/07/17 by Geoffrey Exoo, Milos Tatarevic · 1 citation
Mathematics · Computer Science · #Limits and Structures in Graph Theory #Graph Labeling and Dimension Problems #Advanced Topology and Set Theory #Mathematics #Combinatorics #Ramsey's theorem #Ramsey theory #Heuristic #Greedy coloring #Discrete mathematics #Mathematical optimization #Graph

paper · pdf · doi:10.37236/5254

openalex publication_date 2015/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21

Abstract

We establish new lower bounds for 28 classical two and three color Ramsey numbers, and describe the heuristic search procedures used. Several of the new three color bounds are derived from the two color constructions; specifically, we were able to use (5,k)-colorings to obtain new (3,3,k)-colorings, and (7,k)-colorings to obtain new (3,4,k)-colorings. Some of the other new constructions in the paper are derived from two well known colorings: the Paley coloring of K₁₀₁ and the cubic coloring of K₁₂₇.

Citations

• Small Ramsey Numbers

Cited by

• Ramsey's theorem [wikipedia]

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