On the restricted size Ramsey number for P3 versus dense connected graphs

Denny Riama Silaban (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia)
Edy Tri Baskoro (Combinatorial Mathematics Research Group Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung)
Saladin Uttunggadewa (Combinatorial Mathematics Research Group Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 8, No 2 (2020): Electronic Journal of Graph Theory and Applications

Let F, G and H be simple graphs. A graph F is said a (G,H)-arrowing graph if in any red-blue coloring of edges of F we can find a red G or a blue H. The size Ramsey number of G and H, ŕ(G,H), is the minimum size of F. If the order of F equals to the Ramsey number of G and H, r(G,H), then the minimum size of F is called the restricted size Ramsey number of G and H, r*(G,H). The Ramsey number of G and H, r(G,H), is the minimum order of F. In this paper, we study the restricted size number involving a P3.  The value of r*(P3,Kn) has been given by Faudree and Sheehan. Here, we examine r*(P3,H) where H is dense connected graph.