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Long Monochromatic Berge Cycles in Colored 4-Uniform Hypergraphs

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

Book ID
106047844
Publisher
Springer Japan
Year
2010
Tongue
English
Weight
124 KB
Volume
26
Category
Article
ISSN
0911-0119

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📜 SIMILAR VOLUMES

Monochromatic Hamiltonian 3-tight Berge
Monochromatic Hamiltonian 3-tight Berge cycles in 2-colored 4-uniform hypergraphs
✍ András Gyárfás; Gábor N. Sárközy; Endre Szemerédi 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 122 KB

## 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.

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## 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__ +