Hilda Assiyatun, Budi Rahadjeng, Edy Tri Baskoro
Let F, G, and H be simple graphs. The notation F → (G,H) means that if all the edges of F are arbitrarily colored by red or blue, then there always exists either a red subgraph G or a blue subgraph H: The size Ramsey number of graph G and H, denoted by r(G,H) is the smallest integer k such that there is a graph F with k edges satisfying F → (G,H): In this research, we will study a modified size Ramsey number, namely the connected size Ramsey number. In this case, we only consider connected graphs F satisfying the above properties. This connected size Ramsey number of G and H is denoted by rc(G,H): We will derive an upper bound of rc(nK 2 ,H), n ≥ 2 where H is 2P m or 2K 1,t , and find the exact values of rc(nK 2 ,H), for some fixed n. © 2019 Indonesian Combinatorics Society.
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10, Bandung, Indonesia; Universitas Negeri Surabaya, Indonesia
