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

Gyárfás András | Zendy; Sárközy Gábor N. | Zendy; Szemerédi Endre | Zendy

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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

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