Multipartite Ramsey numbers for the union of stars - I Wayan Palton Anuwiksa; Rinovia Simanjuntak; Edy Tri Baskoro (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2022)
Let s and k be positive integers with k ≥ 2 and G1, G2, …, Gk be simple graphs. The set multipartite Ramsey number, denoted by Ms(G1, G2, …, Gk), is the smallest positive integer c such that any k-coloring of the edges of Kc × s contains a monochromatic copy of Gi in color i for some i ∈ 1, 2, …, k. The size multipartite Ramsey number, denoted by mc(G1, G2, …, Gk), is the smallest positive integer s such that any k-coloring of the edges of Kc × s contains a monochromatic copy of Gi in color i for some i ∈ 1, 2, …, k. In this paper, we establish some lower and upper bounds, and some exact values of multipartite Ramsey numbers for the union of stars.