The Size, Multipartite Ramsey Numbers for nK2 Versus Path–Path and Cycle - Yaser Rowshan; Mostafa Gholami; Stanford Shateyi (Mathematics, 2021)
For given graphs <semantics>G1,G2,…,Gn</semantics> and any integer j, the size of the multipartite Ramsey number <semantics>mj(G1,G2,…,Gn)</semantics> is the smallest positive integer t such that any n-coloring of the edges of <semantics>Kj×t</semantics> contains a monochromatic copy of <semantics>Gi</semantics> in color i for some i, <semantics>1≤i≤n</semantics>, where <semantics>Kj×t</semantics> denotes the complete multipartite graph having j classes with t vertices per each class. In this paper, we computed the size of the multipartite Ramsey numbers <semantics>mj(K1,2,P4,nK2)</semantics> for any <semantics>j,n≥2</semantics> and <semantics>mj(nK2,C7)</semantics>, for any <semantics>j≤4</semantics> and <semantics>n≥2</semantics>.