$R(5,5) \le 48$
Vigleik Angeltveit, Brendan D. McKay
TL;DR
This paper improves the upper bound on the Ramsey number R(5,5) from 49 to 48 and completes the catalog of extremal graphs for R(4,5), advancing combinatorial graph theory knowledge.
Contribution
It provides a tighter upper bound for R(5,5) and completes the extremal graph catalog for R(4,5), offering new insights into Ramsey theory.
Findings
R(5,5) ≤ 48, improving previous bounds
Complete catalog of extremal graphs for R(4,5)
Enhanced understanding of Ramsey numbers
Abstract
We improve the upper bound on the Ramsey number from to . We also complete the catalogue of extremal graphs for .
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Taxonomy
TopicsFinite Group Theory Research