Multipartite Ramsey numbers for the union of stars

I Wayan Palton Anuwiksa (Doctoral Program of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia)
Rinovia Simanjuntak (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia Center for Research Collaboration on Graph Theory and Combinatorics, Indonesia)
Edy Tri Baskoro (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia Center for Research Collaboration on Graph Theory and Combinatorics, Indonesia)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 10, No 2 (2022): Electronic Journal of Graph Theory and Applications

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.