Multicoloured Ramsey numbers of the path of length four

Henry Liu; Bojan Mohar; Yongtang Shi

Multicoloured Ramsey numbers of the path of length four

Combinatorics 2021-08-17 v1

Authors: Henry Liu , Bojan Mohar , Yongtang Shi

Abstract

Let $P_t$ denote the path on $t$ vertices. The $r$ -coloured Ramsey number of $P_t$ , denoted by $R_r(P_t)$ , is the minimum integer $n$ such that whenever the complete graph on $n$ vertices is given an $r$ -edge-colouring, there exists a monochromatic copy of $P_t$ . In this note, we determine $R_r(P_5)$ , which is approximately $3r$ .

Keywords

ramsey number path multicolour edge-colouring complete graph monochromatic copy

Cite

@article{arxiv.2108.06477,
  title  = {Multicoloured Ramsey numbers of the path of length four},
  author = {Henry Liu and Bojan Mohar and Yongtang Shi},
  journal= {arXiv preprint arXiv:2108.06477},
  year   = {2021}
}

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7 pages

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