On Size Bipartite and Tripartite Ramsey Numbers for The Star Forest and Path on 3 Vertices

Anie Lusiani (Politeknik Negeri Bandung, Jalan Gegerkalong Hilir, Ciwaruga, Kabupaten Bandung Barat 40559 Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132)
Edy Tri Baskoro (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132)
Suhadi Wido Saputro (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132)

Journal of Mathematical and Fundamental Sciences
Vol. 52 No. 1 (2020)

For simple graphs G and H the size multipartite Ramsey number mj(G,H) is the smallest natural number t such that any arbitrary red-blue coloring on the edges of Kjxt contains a red G or a blue H as a subgraph. We studied the size tripartite Ramsey numbers m3(G,H) where G=mK1,n and H=P3. In this paper, we generalize this result. We determine m3(G,H) where G is a star forest, namely a disjoint union of heterogeneous stars, and H=P3. Moreover, we also determine m2(G,H) for this pair of graphs G and H.