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Ramsey and Gallai-Ramsey number for wheels

2019/05/28 by Yaping Mao, Zhao Wang, Mao, Yaping +5
Mathematics · #05C55 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C55

paper · pdf · doi:10.48550/arxiv.1905.12414

arXiv admin note: text overlap with arXiv:1809.10298, arXiv:1902.10706

arxiv created 2019/05/28 · arxiv updated 2019/05/30

Abstract

Given a graph G and a positive integer k, define the Gallai-Ramsey number to be the minimum number of vertices n such that any k-edge coloring of Kn contains either a rainbow (all different colored) triangle or a monochromatic copy of G. Much like graph Ramsey numbers, Gallai-Ramsey numbers have gained a reputation as being very difficult to compute in general. As yet, still only precious few sharp results are known. In this paper, we obtain bounds on the Gallai-Ramsey number for wheels and the exact value for the wheel on 5 vertices.

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