Restricted size Ramsey number for 2K2 versus disconnected graphs of order six. Issue 1 (January 2021) - Safitri, E; John, P; Silaban, D R
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 r ˆ such that a graph F with the size of r ˆ 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.