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

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Multipartite Ramsey numbers for the union of stars I Wayan Palton Anuwiksa; Rinovia Simanjuntak; Edy Tri Baskoro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2022.10.2.21

Abstract

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.