Abstract
AbstractLetG1,G2, …,Gtbe arbitrary graphs. The Ramsey numberR(G1,G2, …,Gt) is the smallest positive integernsuch that if the edges of the complete graphKnare partitioned intotdisjoint color classes giving t graphsH1,H2, …,Ht, then at least oneHihas a subgraph isomorphic to Gi. In this paper, we provide the exact value of theR(Tn, Wm) for oddm,n≥m−1, whereTnis either a caterpillar, a tree with diameter at most four, or a tree with a vertex adjacent to at leastleaves, andWnis the wheel onn+ 1 vertices. Also, we determineR(Cn,Wm) for even integersnandm,n≥m+ 500, which improves a result of Shi and confirms a conjecture of Surahmat et al. In addition, the multicolor Ramsey number of trees versus an odd wheel is discussed in this paper.
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