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http://hdl.handle.net/10397/470
Title: | The Ramsey numbers for a cycle of length six or seven versus a clique of order seven | Authors: | Cheng, TCE Chen, Y Zhang, Y Ng, CTD |
Issue Date: | 6-May-2007 | Source: | Discrete mathematics, May 2007, v. 307, no. 9-10, p.1047-1053 | 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. It was conjectured that R(C[sub m],K[sub n])=(m-1)(n-1)+1 for m≥n≥3 and (m,n)≠(3,3). We show that R(C[sub 6],K[sub 7])=31 and R(C[sub 7],K[sub 7])=37, and the latter result confirms the conjecture in the case when m=n=7. | Keywords: | Ramsey number Cycle Complete graph |
Publisher: | Elsevier | Journal: | Discrete mathematics | ISSN: | 0012-365X | EISSN: | 1872-681X | DOI: | 10.1016/j.disc.2006.07.036 | Rights: | Discrete Mathematics © 2006 Elsevier. The journal web site is located at http://www.sciencedirect.com. |
Appears in Collections: | Journal/Magazine Article |
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cczn-1.pdf | Pre-published version | 146.22 kB | Adobe PDF | View/Open |
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