Ramsey numbers of connected 4-clique matchings

Krit Kanopthamakun; Panupong Vichitkunakorn

paper

Ramsey numbers of connected 4-clique matchings

arXiv:2306.08412

Abstract

In this paper, we determine the exact value of the $2$ -edge-coloring Ramsey number of a connected $4$ -clique matching $c (n K_{4})$ , which is a set of connected graphs containing an $n K_{4}$ is $13 n - 3$ for any positive integer $n \geq 3$ . This is an extension of the result by Roberts (2017), which is proved only for $n \geq 18$ . We also show that the result still holds when $n = 2$ provided that $R_{2} (2 K_{4}) \leq 23$ .