Degrees and choice numbers

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58 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)364-368
Number of pages5
JournalRandom Structures and Algorithms
Issue number4
StatePublished - Jul 2000
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • General Mathematics
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics


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