On Ramsey numbers for trees versus fans of even order - Sherlin, Intan; Saputro, Suhadi Wido; Baskoro, Edy Tri; Oktariani, Finny (Indonesian Journal of Combinatorics, 2024)
Given two graphs G and H. The graph Ramsey number R(G, H) is the least natural number r such that for every graph F on r vertices, either F contains a copy of G or F̅ contains a copy of H. A vertex v is called a dominating vertex in a graph G if it is adjacent to all other vertices of G. A wheel Wm is a graph consisting one dominating vertex and m other vertices forming a cycle. A fan graph F1,m is a graph formed from a wheel Wm by removing one cycle-edge. In this paper, we consider the graph Ramsey number R(Tn,F1,m) of a tree Tn versus a fan F1,m. The study of R(Tn,F1,m) has been initiated by Li et. al. (2016) where Tn is a star, and continued by Sherlin et. al. (2023) for Tn which is not a star and fan F1,m with even m ≤ 8. This paper will give the graph Ramsey numbers R(Tn,F1,m) for odd m ≤ 8.