On Ramsey (C4, K1, n)-minimal graphs

Hilda Assiyatun (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia)
Maya Nabila (Doctoral Program of Mathematics, Faculty of Mathematics and Natural Sciences, \\ Institut Teknologi Bandung, Indonesia)
Edy Tri Baskoro (Center for Research Collaboration on Graph Theory and Combinatorics, Indonesia)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 11, No 1 (2023): Electronic Journal of Graph Theory and Applications

Let F, G and H be any simple graphs. The notation F → (G, H) means for any red-blue coloring on the edges of graph F, there exists either a red copy of G or a blue copy of H. If F → (G, H), then graph F is called a Ramsey graph for (G, H). Additionally, if the graph F satisfies that F − e ↛ (G, H) for any edge e of F, then graph F is called a Ramsey (G, H)-minimal. The set of all Ramsey (G, H)-minimal graphs is denoted by ℛ(G, H). In this paper, we construct a new class of Ramsey (C4, K1, n)-minimal graphs.