2021/09/24 by Rowshan, Yaser
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2109.12210
Assume that Kj× n be a complete, multipartite graph consisting of j partite sets and n vertices in each partite set. For given graphs G1, G2,…, Gn, the multipartite Ramsey number (M-R-number) mj(G1, G2, …,Gn) is the smallest integer t such that for any n-edge-coloring (G1,G2,…, Gn) of the edges of Kj× t, Gi contains a monochromatic copy of Gi for at least on i. C. J. Jayawardene, E. T. Baskoro et al. (2016) gave the size of M-R-numbe mj(nK2, C7) for j ≥ 2 and n≤ 6. Y. Rowshan et al. (2021) gave the size of M-R-number mj(nK2, C7) for j = 2,3, 4 and n≥ 2. Y. Rowshan (2021) gave the size of M-R-number mj(nK2,C7), for each j≥ 5 and n≥ 2. In this article we compute the size of M-R-number mj(C3,C3, nK2) for each j≥ 7, n≥ 1, mj(C3,C3, n1K2,n2K_,…,niK2) for each 2≤ j≤ 6, i≥ 2, ni≥ 1, and M-R-number mj(C3,C4, nK2), for each n≥ 1, and small j.