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Monochromatic Hamiltonian 3‐tight Berge cycles in 2‐colored 4‐uniform hypergraphs
Author(s) -
Gyárfás András,
Sárközy Gábor N.,
Szemerédi Endre
Publication year - 2010
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.20427
Subject(s) - monochromatic color , mathematics , combinatorics , conjecture , hamiltonian (control theory) , hamiltonian path , colored , graph , ramsey theory , discrete mathematics , physics , law , mathematical optimization , political science , optics
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 (4) nthere 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