TY - JOUR

T1 - Degrees and choice numbers

AU - Alon, Noga

PY - 2000/7

Y1 - 2000/7

N2 - The choice number ch(G) of a graph G = (V, E) is the minimum number k such that for every assignment of a list S(ν) of at least k colors to each vertex ν ∈ V, there is a proper vertex coloring of G assigning to each vertex ν a color from its list S(ν). We prove that if the minimum degree of G is d, then its choice number is at least (1/2 - 0(1)) log2 d, where the 0(1)-term tends to zero as d tends to infinity. This is tight up to a constant factor of 2 + 0(1), improves an estimate established by the author, and settles a problem raised by him and Krivelevich.

AB - The choice number ch(G) of a graph G = (V, E) is the minimum number k such that for every assignment of a list S(ν) of at least k colors to each vertex ν ∈ V, there is a proper vertex coloring of G assigning to each vertex ν a color from its list S(ν). We prove that if the minimum degree of G is d, then its choice number is at least (1/2 - 0(1)) log2 d, where the 0(1)-term tends to zero as d tends to infinity. This is tight up to a constant factor of 2 + 0(1), improves an estimate established by the author, and settles a problem raised by him and Krivelevich.

UR - http://www.scopus.com/inward/record.url?scp=0034344105&partnerID=8YFLogxK

U2 - 10.1002/1098-2418(200007)16:4<364::AID-RSA5>3.0.CO;2-0

DO - 10.1002/1098-2418(200007)16:4<364::AID-RSA5>3.0.CO;2-0

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AN - SCOPUS:0034344105

SN - 1042-9832

VL - 16

SP - 364

EP - 368

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

IS - 4

ER -