How many random edges make a dense hypergraph non-2-colorable?

2007/07/02 by Sudakov, Benny, Vondrak, Jan
#05D40 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.0707.0315

Abstract

We study a model of random uniform hypergraphs, where a random instance is obtained by adding random edges to a large hypergraph of a given density. We obtain a tight bound on the number of random edges required to ensure non-2-colorability. We prove that for any k-uniform hypergraph with Omega(n^k-epsilon) edges, adding omega(n^{k epsilon/2}) random edges makes the hypergraph almost surely non-2-colorable. This is essentially tight, since there is a 2-colorable hypergraph with Omega(n^k-ε) edges which almost surely remains 2-colorable even after adding o(n^{k ε/ 2}) random edges.

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