TY - JOUR

T1 - Sparse graphs usually have exponentially many optimal colorings

AU - Krivelevich, Michael

PY - 2002

Y1 - 2002

N2 - A proper coloring of a graph G = (V,E) is called optimal if the number of colors used is the minimal possible; i.e., it coincides with the chromatic number of G. We investigate the typical behavior of the number of distinct optimal colorings of a random graph G(n, p), for various values of the edge probability p = p(n). Our main result shows that for every constant 1/3 < a < 2, most of the graphs in the probability space G(n, p) with p = n -a have exponentially many optimal colorings.

AB - A proper coloring of a graph G = (V,E) is called optimal if the number of colors used is the minimal possible; i.e., it coincides with the chromatic number of G. We investigate the typical behavior of the number of distinct optimal colorings of a random graph G(n, p), for various values of the edge probability p = p(n). Our main result shows that for every constant 1/3 < a < 2, most of the graphs in the probability space G(n, p) with p = n -a have exponentially many optimal colorings.

UR - http://www.scopus.com/inward/record.url?scp=4043184124&partnerID=8YFLogxK

U2 - 10.37236/1643

DO - 10.37236/1643

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AN - SCOPUS:4043184124

VL - 9

SP - 1

EP - 8

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

SN - 1077-8926

IS - 1 R

ER -