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The 3-colored Ramsey number of odd cycles

Kohayakawa, Yoshiharu, Simonovits, Miklós and Skokan, Jozef (2005) The 3-colored Ramsey number of odd cycles. Electronic Notes in Discrete Mathematics, 19 (1). pp. 397-402. ISSN 1571-0653

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Abstract

For graphs L1, . . . ,Lk, the Ramsey number R(L1, . . . ,Lk) is the minimum integer N satisfying that for any coloring of the edges of the complete graph KN on N vertices by k colors there exists a color i for which the corresponding color class contains Li as a subgraph. In 1973, Bondy and Erd˝os conjectured that if n is odd and Cn denotes the cy- cle on n vertices, then R(Cn,Cn,Cn) = 4n − 3. In 1999, Luczak proved that R(Cn,Cn,Cn) = 4n + o(n), where o(n)/n ! 0 as n ! 1. In this paper we strengthen Luczak’s result and verify this conjecture for n sufficiently large.

Item Type: Article
Official URL: http://www.sciencedirect.com/science/journal/15710...
Additional Information: © 2005 Elsevier
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Research centres and groups > Computational, Discrete and Applicable Mathematics@LSE (CDAM)
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 20 Jun 2008 08:27
URL: http://eprints.lse.ac.uk/5820/

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