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Two-Coloring Random Hypergraphs Dimitris Achlioptas,1

Summary: Two-Coloring Random Hypergraphs
Dimitris Achlioptas,1
Jeong Han Kim,1
Michael Krivelevich,2
Prasad Tetali3
Microsoft Research, One Microsoft Way, Redmond, WA 98052
Department of Mathematics, Tel Aviv University, Tel Aviv 69978, Israel
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332
Received 8 December 2000; accepted 10 May 2001
ABSTRACT: A 2-coloring 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 k-uniform
hypergraph on a vertex set V of cardinality n, where each k-subset of V is an edge of H
with probability p, independently of all other k-subsets. Let m = p n
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


Source: Achlioptas, Dimitris - Department of Computer Engineering, University of California at Santa Cruz


Collections: Computer Technologies and Information Sciences