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Asymptotic bounds for some bipartite graph: complete graph Ramsey numbers |
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| Authors: | Yair Caro Yusheng Li Cecil C Rousseau Yuming Zhang |
| Institution: | a Department of Mathematics, University of Haifa – Oranim, Tivon 36006, Israel b Department of Mathematics and Physics, Hohai University, Nanjing, Jiangsu 210098, China c Department of Mathematical Sciences, Room 373, Winfield Dunn Building, The University of Memphis, Memphis, TN 38152-3240, USA d Rutcor, Rutgers University, New Brunswick, NJ 08903, USA |
| Abstract: | The Ramsey number r(H,Kn) is the smallest integer N so that each graph on N vertices that fails to contain H as a subgraph has independence number at least n. It is shown that r(K2,m,Kn) (m−1+o(1))(n/log n)2 and r(C2m,Kn)c(n/log n)m/(m−1) for m fixed and n→∞. Also r(K2,n,Kn)=Θ(n3/log2 n) and |
| Keywords: | Ramsey numbers Bipartite graphs Complete graphs |
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