A lower bound for approximating the grundy number

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The grundy number of a graph is the maximum number of colors used by on-line first-fit coloring, under the worst order of arrival of vertices. The grundy number problem is to find this ordering. We prove that there is a constant c > 1 so that approximating the grundy number problem within c is not possible, unless NP ⊆ RP

Original languageEnglish (US)
Pages (from-to)7-22
Number of pages16
JournalDiscrete Mathematics and Theoretical Computer Science
Issue number1
StatePublished - 2007

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)
  • Discrete Mathematics and Combinatorics


  • Approximation
  • Coloring
  • Grundy
  • Hardness
  • Number


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