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

✍ Scribed by András Gyárfás; Gábor N. Sárközy; Endre Szemerédi

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 122 KB
Volume: 63
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20427

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✦ Synopsis

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

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Monochromatic Hamiltonian t-tight Berge-cycles in hypergraphs

✍ Paul Dorbec; Sylvain Gravier; Gábor N. Sárközy 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 141 KB

## Abstract In any __r__‐uniform hypergraph ${\cal{H}}$ for 2 ≤ __t__ ≤ __r__ we define an __r__‐uniform __t__‐tight Berge‐cycle of length ℓ, denoted by __C__~ℓ~^(__r__, __t__)^, as a sequence of distinct vertices __v__~1~, __v__~2~, … , __v__~ℓ~, such that for each set (__v__~__i__~, __v__~__i__ +