The Ramsey numbers for stars of even order versus a wheel of order nine
For two graphs \(G_1,G_2\) the Ramsey number \(R(G_1,G_2)\) is the least \(n\) such that every red-blue edge coloring of the complete \(n\)-vertex graph contains either red \(G_1\) or blue \(G_2\). The notation \(S_m\) denotes the star on \(m\) vertices, and \(W_m\) stands for the wheel graph on \(m+1\) vertices. The paper shows that \(R(S_n,W_8)=2n+2\) for \(n\geq 6\) and \(n\equiv 0 \pmod 2\). The values of \(R(S_n,W_m)\) for odd \(m\) and \(n\geq m-1\) were previously determined by \textit{Y. Chen, Y. Zhang} and \textit{K. Zhang} [``The Ramsey numbers of stars versus wheels,'' Eur. J. Comb. 25, No. 7, 1067--1075 (2004; Zbl 1050.05087)], and the values of \(R(S_n,W_4)\) were determined by Surahmat and Baskoro [``On the Ramsey number of path or star versus \(W_4\) or \(W_5\)'', in: Proceedings of the 12th Australasian Workshop on Combinatorial Algorithms, Bandung, Indonesia, 14-17 July 2001, 174--179].
scientific article; zbMATH DE number 5321381