Restricted size Ramsey number for 2K 2 versus disconnected graphs of order six

Abstract

Given simple graphs F, G, and H. We say F arrows (G, H) if for any red-blue coloring of the edge of F, we find either a red-colored graph G or a blue-colored graph H. The Ramsey number r(G, H) is the smallest positive integer r such that a complete graph K r arrows (G, H). The size Ramsey number is the smallest positive integer such that a graph F with the size of arrows (G, H). The restricted size Ramsey number is the smallest positive integer r ∗ such that a graph F, of order r(G, H) with the size of r ∗, arrows (G, H). In this paper we give the restricted size Ramsey number of a matching of two edges and any disconnected graphs of order six with no isolates.