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On Contact Graphs of Paths on a Grid

  • Zakir Deniz
  • Esther GalbyEmail author
  • Andrea Munaro
  • Bernard Ries
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11282)

Abstract

In this paper we consider Contact graphs of Paths on a Grid (CPG graphs), i.e. graphs for which there exists a family of interiorly disjoint paths on a grid in one-to-one correspondence with their vertex set such that two vertices are adjacent if and only if the corresponding paths touch at a grid-point. Our class generalizes the well studied class of VCPG graphs (see [1]). We examine CPG graphs from a structural point of view which leads to constant upper bounds on the clique number and the chromatic number. Moreover, we investigate the recognition and 3-colorability problems for \(B_0\)-CPG, a subclass of CPG. We further show that CPG graphs are not necessarily planar and not all planar graphs are CPG.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Zakir Deniz
    • 1
  • Esther Galby
    • 2
    Email author
  • Andrea Munaro
    • 2
  • Bernard Ries
    • 2
  1. 1.Department of MathematicsDuzce UniversityDuzceTurkey
  2. 2.Department of Informatics, Decision Support & Operations ResearchUniversity of FribourgFribourgSwitzerland

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