Diagonal Ramsey numbers in multipartite graphs related to stars

Chula Janak Jayawardene (University of Colombo, Colombo\ Sri Lanka)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 10, No 1 (2022): Electronic Journal of Graph Theory and Applications

Abstract: Let the star on n vertices, namely K1, n − 1 be denoted by Sn. If every two coloring of the edges of a complete balanced multipartite graph Kj × s there is a copy of Sn in the first color or a copy of Sm in the second color, then we will say Kj × s → (Sn, Sm). The size Ramsey multipartite number mj(Sn, Sm) is the smallest natural number s such that Kj × s → (Sn, Sm). In this paper, we obtain the exact values of the size Ramsey numbers mj(Sn, Sm) for n, m ≥ 3 and j ≥ 3.