Restricted Size Ramsey Number for Matching versus Tree and Triangle Unicyclic Graphs of Order Six

Elda Safitri (University of Indonesia)
Peter John (University of Indonesia)
Denny Riama Silaban (University of Indonesia)

International Journal of Computing Science and Applied Mathematics
Vol 8, No 1 (2022)

Let F, G, and H be simple graphs. The graph F arrows (G,H) if for any red-blue coloring on the edge of F, we find either a red-colored graph G or a blue-colored graph H in F. The Ramsey number r(G,H) is the smallest positive integer r such that a complete graph Kr arrows (G,H). The restricted size Ramsey number r∗(G,H) is the smallest positive integer r∗ such that there is a graph F, of order r(G,H) and with the size r∗, satisfying F arrows (G,H). In this paper we give the restricted size Ramsey number for a matching of two edges versus tree and triangle unicyclic graphs of order six.