Coloring intersection graphs of x-monotone curves in the plane

Abstract

A class of graphs G is χ-bounded if the chromatic number of the graphs in G is bounded by some function of their clique number. We show that the class of intersection graphs of simple families of x-monotone curves in the plane intersecting a vertical line is χ-bounded. As a corollary, we show that the class of intersection graphs of rays in the plane is χ-bounded, and the class of intersection graphs of unit segments in the plane is χ-bounded.

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Correspondence to Andrew Suk.

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Supported by an NSF Postdoctoral Fellowship.

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Suk, A. Coloring intersection graphs of x-monotone curves in the plane. Combinatorica 34, 487–505 (2014). https://doi.org/10.1007/s00493-014-2942-5

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Mathematics Subject Classification (2000)

  • 05C15
  • 52C10