First-Fit coloring of bounded tolerance graphs

  • Authors:

  • H. A. Kierstead;Karin R. Saoub

  • Affiliations:

  • Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, USA;Department of Mathematics, Computer Science and Physics, Roanoke College, Salem, VA 24153, USA

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2011

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Abstract

Let G=(V,E) be a graph. A tolerance representation of G is a set I={I"v:v@?V} of intervals and a set t={t"v:v@?V} of nonnegative reals such that xy@?E iff I"x@?I"y0@? and @?I"x@?I"y@?=min{t"x,t"y}; in this case G is a tolerance graph. We refine this definition by saying that G is a p-tolerance graph if t"v/|I"v|@?p for all v@?V. A Grundy coloring g of G is a proper coloring of V with positive integers such that for every positive integer i, if i