 
Summary: TwoColoring Random Hypergraphs
Dimitris Achlioptas,1
Jeong Han Kim,1
Michael Krivelevich,2
Prasad Tetali3
1
Microsoft Research, One Microsoft Way, Redmond, WA 98052
2
Department of Mathematics, Tel Aviv University, Tel Aviv 69978, Israel
3
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332
Received 8 December 2000; accepted 10 May 2001
ABSTRACT: A 2coloring of a hypergraph is a mapping from its vertex set to a set of two
colors such that no edge is monochromatic. Let H = H k n p be a random kuniform
hypergraph on a vertex set V of cardinality n, where each ksubset of V is an edge of H
with probability p, independently of all other ksubsets. Let m = p n
k
denote the expected
number of edges in H. Let us say that a sequence of events n holds with high probability
(w.h.p.) if limn Pr n = 1. It is easy to show that if m = c2k
