Gallai-Ramsey numbers for graphs with five vertices of chromatic number four

Qinghong Zhao; Bing Wei

Gallai-Ramsey numbers for graphs with five vertices of chromatic number four

Combinatorics 2021-07-15 v1

Authors: Qinghong Zhao , Bing Wei

Abstract

Given a graph $H$ and an integer $k\ge1$ , the Gallai-Ramsey number $GR_k(H)$ is defined to be the minimum integer $n$ such that every $k$ -edge coloring of $K_n$ contains either a rainbow (all different colored) triangle or a monochromatic copy of $H$ . In this paper, we determine the Gallai-Ramsey numbers for connected graphs with five vertices of chromatic number four.

Keywords

gallai-ramsey number edge coloring rainbow triangle monochromatic copy chromatic number complete graph

Cite

@article{arxiv.2008.00361,
  title  = {Gallai-Ramsey numbers for graphs with five vertices of chromatic number four},
  author = {Qinghong Zhao and Bing Wei},
  journal= {arXiv preprint arXiv:2008.00361},
  year   = {2021}
}

Comments

18 pages, 1 figure. arXiv admin note: text overlap with arXiv:2006.02603

Gallai-Ramsey numbers for graphs with five vertices of chromatic number four

Abstract

Keywords

Cite

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