New lower bounds for two color and multicolor Ramsey numbers
Robert Gerbicz
TL;DR
This paper establishes new lower bounds for various two-color and multicolor Ramsey numbers using cyclic graphs, improving upon previous known bounds and advancing understanding in combinatorial mathematics.
Contribution
The paper introduces novel lower bounds for specific two-color and multicolor Ramsey numbers using cyclic graph constructions, surpassing previous results.
Findings
R(4,16)>163
R(5,11)>170
R(5,12)>190
Abstract
Using cyclic graphs I give new lower bounds for two color and multicolor Ramsey numbers: R(4,16)>163, R(5,11)>170, R(5,12)>190, R(5,13)>212, R(5,14)>238, R(3,3,9)>117, R(3,3,10)>141 and R(3,3,11)>157. Improving the previous best known bounds.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Topology and Set Theory · Computability, Logic, AI Algorithms