Abstract
For two given graphs \(G_1\) and \(G_2\), the Ramsey number \(R(G_1,G_2)\) is the smallest integer n such that for any graph G of order n, either G contains \(G_1\) or \({\overline{G}}\) contains \(G_2\). Let \(T_n\) denote a tree of order n, and a generalized wheel \(K_s + C_m\) is the graph obtained by joining each vertex of \(K_s\) to each vertex of \(C_m\). In this paper, we show that: \(R(T_n,K_s+ C_6)=(s+1)(n-1)+1\) for \(s\ge 2\) and \(n\ge 5\), and \(R(T_n,K_s+ C_7)=(s+2)(n-1)+1\) for \(s\ge 1\) and \(n\ge 5\).
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Wang, L. The Ramsey Numbers of Trees Versus Generalized 6-Wheels or Generalized 7-Wheels. Graphs and Combinatorics 38, 153 (2022). https://doi.org/10.1007/s00373-022-02533-8
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DOI: https://doi.org/10.1007/s00373-022-02533-8