Restricted Size Ramsey Number Involving Matching and Graph of Order Five

Denny Riama Silaban (2Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok 16424,)
Edy Tri Baskoro (Combinatorial Mathematics Research Group Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung, Jalan Ganesa 10 Bandung 40132)
Saladin Uttunggadewa (Combinatorial Mathematics Research Group Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung, Jalan Ganesa 10 Bandung 40132)

Journal of Mathematical and Fundamental Sciences
Vol. 52 No. 2 (2020)

Harary and Miller (1983) started the research on the (restricted) size Ramsey number for a pair of small graphs. They obtained the values for some pairs of small graphs with order not more than four. In the same year, Faudree and Sheehan continued the research and extended the result to all pairs of small graphs with order not more than four. Moreover, in 1998, Lortz and Mengenser gave the size Ramsey number and the restricted size Ramsey number for all pairs of small forests with order not more than five. Recently, we gave the restricted size Ramsey number for a path of order three and any connected graph of order five. In this paper, we continue the research on the (restricted) size Ramsey number involving small graphs by investigating the restricted size Ramsey number for matching with two edges versus any graph of order five with no isolates.