Long monochromatic Berge cycles in colored 4-uniform hypergraphs
A Gyárfás, GN Sárközy, E Szemerédi - Graphs and Combinatorics, 2010 - Springer
A Gyárfás, GN Sárközy, E Szemerédi
Graphs and Combinatorics, 2010•SpringerHere we prove that for n≥ 140, in every 3-coloring of the edges of K_n^(4) there is a
monochromatic Berge cycle of length at least n− 10. This result sharpens an asymptotic
result obtained earlier. Another result is that for n≥ 15, in every 2-coloring of the edges of
K_n^(4) there is a 3-tight Berge cycle of length at least n− 10.
monochromatic Berge cycle of length at least n− 10. This result sharpens an asymptotic
result obtained earlier. Another result is that for n≥ 15, in every 2-coloring of the edges of
K_n^(4) there is a 3-tight Berge cycle of length at least n− 10.
Abstract
Here we prove that for n ≥ 140, in every 3-coloring of the edges of there is a monochromatic Berge cycle of length at least n − 10. This result sharpens an asymptotic result obtained earlier. Another result is that for n ≥ 15, in every 2-coloring of the edges of there is a 3-tight Berge cycle of length at least n − 10.
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