Subdivision of graphs in [Formula: see text]

For any graphs [Formula: see text] , and H, the notation [Formula: see text] 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 [Formula: see text] consists of all Ramsey [Formula: see text]-minimal graphs, namely all graphs F satisfying [Formula: see text] but for each [Formula: see text] , [Formula: see text]. 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 [Formula: see text] and let [Formula: see text] be an edge contained in a cycle of F, we construct a new Ramsey minimal graph in [Formula: see text] from graph F by subdividing the edge e four times.