TY - JOUR

T1 - Two-Coloring Random Hypergraphs

AU - Achlioptas, Dimitris

AU - Kim, Jeong Han

AU - Krivelevich, Michael

AU - Tetali, Prasad

PY - 2002/3

Y1 - 2002/3

N2 - 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(kn) denote the expected number of edges in H. Let us say that a sequence of events ℰn holds with high probability (w.h.p.) if limn→∞Pr[ℰn] = 1. It is easy to show that if m = c2kn then w.h.p H is not 2-colorable for c > In 2/2. We prove that there exists a constant c > 0 such that if m = (c2 k/k)n, then w.h.p H is 2-colorable.

AB - 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(kn) denote the expected number of edges in H. Let us say that a sequence of events ℰn holds with high probability (w.h.p.) if limn→∞Pr[ℰn] = 1. It is easy to show that if m = c2kn then w.h.p H is not 2-colorable for c > In 2/2. We prove that there exists a constant c > 0 such that if m = (c2 k/k)n, then w.h.p H is 2-colorable.

UR - http://www.scopus.com/inward/record.url?scp=0036103236&partnerID=8YFLogxK

U2 - 10.1002/rsa.997

DO - 10.1002/rsa.997

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AN - SCOPUS:0036103236

SN - 1042-9832

VL - 20

SP - 249

EP - 259

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

IS - 2

ER -