On size tripartite Ramsey numbers of P 3 versus mK 1,n

• Main Authors: Lusiani, Anie, Baskoro, Edy Tri, Saputro, Suhadi Wido
• Format: Conference Proceeding
• Language: English
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/1.4940811

Let Kl×t be a complete, balanced, multipartite graph consisting of l partite sets and t vertices in each partite set. For simple graphs G and H, the size multipartite Ramsey number m j (G, H) is the smallest natural number t such that any arbitrary red-blue coloring on the edges of Kl×t contains a red G or a blue H as a subgraph. In particular, if j = 3 then m 3(G, H) is called the size tripartite Ramsey number of G and H. In this paper, we determine the exact values of the size tripartite numbers m 3(P 3, mK 1,n ) for all integers m ≥ 1 and n ≥ 3, where P 3 is a path of order 3 and mK 1,n is a disjoint union of m copies of a star K 1,n .