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Tight Hamilton cycles in random uniform hypergraphs

✍ Scribed by Andrzej Dudek; Alan Frieze

Book ID
112187383
Publisher
John Wiley and Sons
Year
2012
Tongue
English
Weight
123 KB
Volume
42
Category
Article
ISSN
1042-9832

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## 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__ +