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 -