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On the Intersection Graphs of Orthogonal Line Segments in the Plane: Characterizations of Some Subclasses of Chordal Graphs

Abstract

We investigate here the intersection graphs of horizontal and vertical line segments in the plane, the so called B 0-VPG graphs. A forbidden induced subgraph characterization of B 0-VPG split graphs is given, and we present a linear time algorithm to recognize this class. Next, we characterize chordal bull-free B 0-VPG graphs and chordal claw-free B 0-VPG graphs.

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Correspondence to B. Ries.

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This paper is dedicated to the memories of Bruno Simeone and Peter L. Hammer.

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Golumbic, M.C., Ries, B. On the Intersection Graphs of Orthogonal Line Segments in the Plane: Characterizations of Some Subclasses of Chordal Graphs. Graphs and Combinatorics 29, 499–517 (2013). https://doi.org/10.1007/s00373-012-1133-7

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  • DOI: https://doi.org/10.1007/s00373-012-1133-7

Keywords

  • 2-DIR graphs
  • Segment graphs
  • Vertex intersection graph
  • Rectangular grid
  • Split graphs
  • Chordal bull-free graphs
  • Chordal claw-free graphs