Subdivision of graphs in

For any graphs $$ , and H, the notation $$ means that any red-blue coloring of all edges of F will contain either a red copy of G or a blue copy of H. The set $$ consists of all Ramsey $$ -minimal graphs, namely all graphs F satisfying $$ but for each $$ , $$ . In this paper, we propose a simple construction for creating new Ramsey minimal graphs from the previous known Ramsey minimal graphs (by subdivision operation). In particular, suppose $$ and let $$ be an edge contained in a cycle of F, we construct a new Ramsey minimal graph in $$ from graph F by subdividing the edge e four times.