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Title: | The Ramsey numbers R(C[sub m], K[sub 7]) and R(C[sub 7], K[sub 8]) | Authors: | Chen, Y Cheng, TCE Zhang, Y |
Issue Date: | Jul-2008 | Source: | European journal of combinatorics, July 2008, v. 29, no. 5, p. 1337-1352 | Abstract: | For two given graphs G₁ and G₂, the Ramsey number R(G₁, G₂) is the smallest integer n such that for any graph G of order n, either G contains G₁ or the complement of G contains G₂. Let C[sub m] denote a cycle of length m and K[sub n] a complete graph of order n. In this paper we show that R(C[sub m], K[sub 7]) = 6m − 5 for m ≥ 7 and R(C[sub 7], K[sub 8]) = 43, with the former result confirming a conjecture due to Erdös, Faudree, Rousseau and Schelp that R(C[sub m], K[sub n]) = (m − 1)(n − 1)+ 1 for m ≥ n ≥ 3 and (m,n) ≠ (3,3) in the case where n = 7. | Keywords: | Ramsey number Complete graph |
Publisher: | Academic Press | Journal: | European journal of combinatorics | ISSN: | 0195-6698 | DOI: | 10.1016/j.ejc.2007.05.007 | Rights: | European Journal of Combinatorics © 2007 Elsevier Ltd. The journal web site is located at http://www.sciencedirect.com. |
Appears in Collections: | Journal/Magazine Article |
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EJC2804.pdf | Pre-published version | 240.09 kB | Adobe PDF | View/Open |
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