For graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest integer N such that, for any graph G of order N, G contains G1 as a subgraph or the complement of G contains G2 as a subgraph. Let Tn denote a tree of order n, Wn a wheel of order n+1 and Fn a fan of order 2n+1. We establish Ramsey numbers for fans and trees versus wheels of even order, thereby extending several known results. In particular, we prove that R(Fn,Wm)=6n+1 for odd m≥3 and n≥(5m+3)/4, and that R(Tn,Wm)=3n−2 for odd m≥3 and n≥m−2, and Tn being a tree for which the Erdős–Sós Conjecture holds.
- Ramsey number