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Representations by Contact and Intersection of Segments

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Abstract

A necessary and sufficient condition is given for a connected bipartite graph to be the incidence graph of a contact family of segments and points. We deduce that any four-connected three-colorable plane graph is the contact graph of a family of segments and that any four-colored planar graph without an induced C4 using four colors is the intersection graph of a family of straight line segments.

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Authors and Affiliations

  1. Centre d'Analyse et de Mathematique Sociales, CNRS UMR 8557, Ecole des Hautes Etudes en Sciences Sociales, 54 Boulevard Raspail, 75006, Paris, France

    Hubert de Fraysseix & Patrice Ossona de Mendez

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  1. Hubert de Fraysseix
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  2. Patrice Ossona de Mendez
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Correspondence to Hubert de Fraysseix or Patrice Ossona de Mendez.

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de Fraysseix, H., de Mendez, P. Representations by Contact and Intersection of Segments. Algorithmica 47, 453–463 (2007). https://doi.org/10.1007/s00453-006-0157-x

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  • DOI: https://doi.org/10.1007/s00453-006-0157-x

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