Restricted size Ramsey numbers and restricted size Ramsey minimal graphs for matching versus wheel upto order six

Abstract

The notion of the restricted size Ramsey number arises from the amalgamation of the theory of Ramsey numbers and the size Ramsey number for graphs. The concept of the (restricted) size Ramsey number of small graphs was first introduced by Harary and Miller in 1983. They derived specific values for certain pairs of small graphs, each having a maximum count of four vertices. In that same year, R. J. Faudree and J. Sheehan furthered the research and expanded the findings to encompass all the pairs of small graphs with a maximum order of four. The restricted size Ramsey number and size Ramsey number for all pairs of small forests of maximum order five was given by Lortz and Mengersen in 1998. In this study, our research endeavours to advance the understanding of the restricted size Ramsey number by ascertaining the restricted size Ramsey numbers and restricted size Ramsey minimal graphs involving 2K2 and wheel graph upto order six. More specifically, we find r * (2K2, W3) = r* (2K2, W4) = 15 and r * (2K2, W5) = 19.