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

## 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 |
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Official URL: | http://www.sciencedirect.com/science/journal/15710... |

Additional Information: | © 2005 Elsevier |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics Research centres and groups > Computational, Discrete and Applicable Mathematics@LSE (CDAM) |

Date Deposited: | 20 Jun 2008 08:27 |

Last Modified: | 21 Apr 2019 23:07 |

URI: | http://eprints.lse.ac.uk/id/eprint/5820 |

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