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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,...
For two given graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest integer N such that, for any graph G of order N, either G contains G1 as a subgraph or the complement of G contains G2 as a subgraph. Let Tn be a tree of order n, Sn a star of order n, and Fm a fan of order 2m+1, i.e., m triangles sharing exactly one vertex. In this paper, we prove that R(Tn,Fm)=2n−1 for n≥3m2−2m−1, and if...
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