Let K l×t be a complete, balanced, multipartite graph consisting of l partite sets and t vertices in each partite set. For given two graphs G 1 and G 2 , and integer j ≥ 2, the size multipartite Ramsey number m j (G 1 , G 2 ) is the smallest integer t such that every factorization of the graph K j×t := F 1 ⊕ F 2 satisfies the following condition: either F 1 contains G 1 or F 2 contains G 2 . In 2007, Syafrizal et al. determined the size multipartite Ramsey numbers of paths P n versus stars, for n = 2, 3 only. Furthermore, Surahmat et al. (2014) gave the size tripartite Ramsey numbers of paths P n versus stars, for n = 3, 4, 5, 6. In this paper, we investigate the size tripartite Ramsey numbers of paths P n versus stars, with all n ≥ 2. Our results complete the previous results given by Syafrizal et al. and Surahmat et al. We also determine the size bipartite Ramsey numbers m 2 (K 1,m , C n ) of stars versus cycles, for n ≥ 3, m ≥ 2.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.