Monochromatic Hamiltonian 3‐tight Berge cycles in 2‐colored 4‐uniform hypergraphs

András Gyárfás; Gábor N. Sárközy; Endre Szemerédi

doi:10.1002/jgt.20427

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Monochromatic Hamiltonian 3‐tight Berge cycles in 2‐colored 4‐uniform hypergraphs

András Gyárfás Gábor N. Sárközy Endre Szemerédi

Year: 2009 Journal: Journal of Graph Theory Vol: 63 (4)Pages: 288-299 Publisher: Wiley

DOI: 10.1002/jgt.20427

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Abstract

Abstract Here improving on our earlier results, we prove that there exists an n 0 such that for n ⩾ n 0 in every 2‐coloring of the edges of K there is a monochromatic Hamiltonian 3‐tight Berge cycle. This proves the c =2, t =3, r =4 special case of a conjecture from (P. Dorbec, S. Gravier, and G. N. Sárközy, J Graph Theory 59 (2008), 34–44). © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 288–299, 2010

Keywords:

Monochromatic color Mathematics Combinatorics Conjecture Hamiltonian (control theory) Hamiltonian path Colored Graph Ramsey theory Discrete mathematics Physics Law

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Limits and Structures in Graph Theory

Physical Sciences → Mathematics → Discrete Mathematics and Combinatorics

graph theory and CDMA systems

Physical Sciences → Engineering → Electrical and Electronic Engineering

Advanced Graph Theory Research

Physical Sciences → Computer Science → Computational Theory and Mathematics

Monochromatic Hamiltonian 3‐tight Berge cycles in 2‐colored 4‐uniform hypergraphs

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