Tales of Hoffman: three extensions of Hoffman's bound on the graph chromatic number

  • Authors:

  • Yonatan Bilu

  • Affiliations:

  • Department of Molecular Genetics, Weizmann Institute of Science, Rehovot, Israel

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2006

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Abstract

Hoffman's bound on the chromatic number of a graph states that χ ≥ 1 -λ1/λn. Here we show that the same bound, or slight modifications of it, hold for several graph parameters related to the chromatic number: the vector coloring number, the ψ-covering number and the λ-clustering number.