Ramsey goodness and generalized stars

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• 作者：Qizhong Lin ; Yusheng Li ; Lin Dong
• 刊名：European Journal of Combinatorics
• 出版年：2010
• 出版时间：July 2010
• 年：2010
• 卷：31
• 期：5
• 页码：1228-1234
• 全文大小：272 K

文摘

Let G and H be fixed graphs with s(G)=s (the minimum number of vertices in a color class over all proper vertex-colorings of G with χ(G) colors). It is shown that r(K₁+G,K₁+nH)≤k(hn+s−1)+1 for large n, where χ(G)=k≥2. In particular, if s is odd or s is even and hn is odd, then r(K₁+K_k(s),K₁+nH)=k(hn+s−1)+1, where K_k(s) is a complete k-partite graph with s vertices in each part, implying that K₁+nH is not (K₁+K_k(s))-good. Moreover, r(K₁+sK₂,K₁+nH)=2hn+1 for large n.