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A multipartite Ramsey number for odd cycles
Author(s) -
Benevides Fabrıcio Siqueira
Publication year - 2012
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.20647
Subject(s) - multipartite , mathematics , combinatorics , conjecture , ramsey's theorem , graph , monochromatic color , discrete mathematics , integer (computer science) , quantum , computer science , physics , quantum mechanics , quantum entanglement , optics , programming language
In this article we study multipartite Ramsey numbers for odd cycles. Our main result is the proof that a conjecture of Gyárfás et al. (J Graph Theory 61 (2009), 12–21), holds for graphs with a large enough number of vertices. Precisely, there exists n 0 such that if n ⩾ n 0 is a positive odd integer then any two‐coloring of the edges of the complete five‐partite graph K ( n − 1)/2, ( n − 1)/2, ( n − 1)/2, ( n − 1)/2, 1 contains a monochromatic cycle of length n . © 2011 Wiley Periodicals, Inc. J Graph Theory
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