Large monochromatic components and long monochromatic cycles in random hypergraphs

2017/09/09 by Patrick Bennett, Bennett, Patrick, Louis DeBiasio +5
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1709.02990

arxiv created 2018/07/26 · arxiv updated 2018/07/27

Abstract

We extend results of Gyárfás and Füredi on the largest monochromatic component in r-colored complete k-uniform hypergraphs to the setting of random hypergraphs. We also study long monochromatic loose cycles in r-colored random hypergraphs. In particular, we obtain a random analog of a result of Gyárfás, Sárközy, and Szemerédi on the longest monochromatic loose cycle in 2-colored complete k-uniform hypergraphs.

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