%0 Journal Article
%T Monochromatic Hamiltonian Berge-cycles in colored hypergraphs
%A G. R. Omidi
%A L. Maherani
%J Mathematics
%D 2014
%I arXiv
%X 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].
%U http://arxiv.org/abs/1403.2894v1