The size, multipartite Ramsey numbers for nK2 versus path-path and cycle

2021/01/03 by Rowshan, Yaser, Gholami, Mostafa
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2101.00617

Abstract

For given graphs G₁, G₂,…, G_n and any integer j, the size of the multipartite Ramsey number m_j(G₁, G₂,…, G_n) is the smallest positive integer t such that any n-coloring of the edges of K_{j× t} contains a monochromatic copy of G_i in color i for some i, 1 ≤ i ≤ n, where K_{j× t} denotes the complete multipartite graph having j classes with t vertices per each class. In this paper we compute the size of the multipartite Ramsey number m_j(K_1,2, P₄, nK₂) for any j,n≥ 2 and m_j(nK₂,C₇), for any j≤4 and n≥ 2.

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