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
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
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 -