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| Paper IPM / M / 14712 |
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| Abstract: | |
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It has been conjectured that for any fixed r and sufficiently large n, there is a monochromatic
Hamiltonian Berge-cycle in every (r â 1)-coloring of the edges of Krn, the complete
r-uniform hypergraph on n vertices. In this paper, we show that the statement of this
conjecture is true with r â 2 colors (instead of r â 1 colors) by showing that there is a
monochromatic Hamiltonian t-tight Berge-cycle in every â râ2
tâ1 â-edge-coloring of Krn
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 Dorbec et al.
(2008) and Gyárfás et al. (2008, 2010).
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