Monochromatic Hamiltonian Berge-cycles in colored hypergraphs
Combinatorics
2014-03-13 v1
Abstract
It has been conjectured that for any fixed r and sufficiently large n, there is a monochromatic Hamiltonian Berge-cycle in every (r - 1)-coloring of the edges of the complete r-uniform hypergraph on n vertices. In this paper, we show that the statement of this conjecture is true with r-2 colors (instead of r-1 colors) by showing that there is a monochromatic Hamiltonian t-tight Berge-cycle in every b r-2 / t-1 -edge coloring of Kr n for any fixed r > t >= 2 and sufficiently large n. Also, we give a proof for this conjecture when r = 4 (the first open case). These results improve the previously known results in [2, 3, 4].
Cite
@article{arxiv.1403.2894,
title = {Monochromatic Hamiltonian Berge-cycles in colored hypergraphs},
author = {G. R. Omidi and L. Maherani},
journal= {arXiv preprint arXiv:1403.2894},
year = {2014}
}