Abstract
Here 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.
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A. Gyárfás was supported in part by OTKA Grant No. K68322. G. N. Sárközy was supported in part by the National Science Foundation under Grant No. DMS-0456401, by OTKA Grant No. K68322 and by a János Bolyai Research Scholarship.
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Gyárfás, A., Sárközy, G.N. & Szemerédi, E. Long Monochromatic Berge Cycles in Colored 4-Uniform Hypergraphs. Graphs and Combinatorics 26, 71–76 (2010). https://doi.org/10.1007/s00373-010-0908-y
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DOI: https://doi.org/10.1007/s00373-010-0908-y