Size multipartite Ramsey numbers for small paths versus books - Chula J. Jayawardene; Jayampathy Ratnayake (Indonesian Combinatorial Society (InaCombS), 2016)
Given j 2, for graphs G and H, the size Ramsey multipartite number m_j(G, H) is defined as the smallest natural number t such that any blue red coloring of the edges of the graph K_j × t, necessarily containes a red G or a blue H as subgraphs. Let the book with n pages is defined as the graph K_1 + K_1,n and denoted by B_n. In this paper, we obtain the exact values of the size Ramsey numbers m_j(P_3, H) for j 3 where H is a book B_n. We also derive some upper and lower bounds for the size Ramsey numbers m_j(P_4, H) where H is a book B_n.