TY - JOUR

T1 - List coloring of random and pseudo-random graphs

AU - Alon, Noga

AU - Krivelevich, Michael

AU - Sudakov, Benny

N1 - Funding Information:
Mathem atics Subject Classification (1991): 05C80, 05C15 * Research supported in part by a USA Israeli BSF grant and by a Science Foundation. † Research supported in part by a Charles Clore Fellowship.

PY - 1999

Y1 - 1999

N2 - The choice number of a graph G is the minimum integer k such that for every assignment of a set S(v) of k colors to every vertex v of G, there is a proper coloring of G that assigns to each vertex v a color from S(v). It is shown that the choice number of the random graph G(n,p(n)) is almost surely θ ( np(n)/ln(np(n)) whenever 2 < np(n) ≤ n/2. A related result for pseudo-random graphs is proved as well. By a special case of this result, the choice number (as well as the chromatic number) of any graph on n vertices with minimum degree at least n/2 - n0.99 in which no two distinct vertices have more than n/44+n0.99 common neighbors is at most O(n/lnn).

AB - The choice number of a graph G is the minimum integer k such that for every assignment of a set S(v) of k colors to every vertex v of G, there is a proper coloring of G that assigns to each vertex v a color from S(v). It is shown that the choice number of the random graph G(n,p(n)) is almost surely θ ( np(n)/ln(np(n)) whenever 2 < np(n) ≤ n/2. A related result for pseudo-random graphs is proved as well. By a special case of this result, the choice number (as well as the chromatic number) of any graph on n vertices with minimum degree at least n/2 - n0.99 in which no two distinct vertices have more than n/44+n0.99 common neighbors is at most O(n/lnn).

UR - http://www.scopus.com/inward/record.url?scp=0040113658&partnerID=8YFLogxK

U2 - 10.1007/s004939970001

DO - 10.1007/s004939970001

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AN - SCOPUS:0040113658

SN - 0209-9683

VL - 19

SP - 453

EP - 472

JO - Combinatorica

JF - Combinatorica

IS - 4

ER -