On Ramsey -minimal graphs

Abstract

Let and be simple graphs. We write to mean that any red–blue coloring of all edges of will contain either a red copy of or a blue copy of A graph (without isolated vertices) satisfying and for each is called a Ramsey -minimal graph. The set of all Ramsey -minimal graphs is denoted by In this paper, we derive the necessary and sufficient condition of graphs belonging to for any connected graph Moreover, we give a relation between Ramsey - and -minimal graphs, and Ramsey - and -minimal graphs. Furthermore, we determine all graphs in

Keywords

• ramsey minimal graph
• edge coloring
• matching
• path