Multicoloured Ramsey numbers of the path of length four
Henry Liu, Bojan Mohar, Yongtang Shi

TL;DR
This paper determines the multicoloured Ramsey number for the path of length four, showing it is approximately three times the number of colours, advancing understanding of colourings in complete graphs.
Contribution
The paper explicitly calculates the multicoloured Ramsey number for the path of length four, filling a gap in combinatorial graph theory.
Findings
$R_r(P_5)$ is approximately $3r$
Provides exact values for multicoloured Ramsey numbers of $P_5$
Enhances understanding of colourings in complete graphs
Abstract
Let denote the path on vertices. The -coloured Ramsey number of , denoted by , is the minimum integer such that whenever the complete graph on vertices is given an -edge-colouring, there exists a monochromatic copy of . In this note, we determine , which is approximately .
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Topology and Set Theory · Graph Labeling and Dimension Problems
