Bend-Bounded Path Intersection Graphs: Sausages, Noodles, and Waffles on a Grill

  • Steven Chaplick
  • Vít Jelínek
  • Jan Kratochvíl
  • Tomáš Vyskočil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7551)


In this paper we study properties of intersection graphs of k-bend paths in the rectangular grid. A k-bend path is a path with at most k 90 degree turns. The class of graphs representable by intersections of k-bend paths is denoted by B k -VPG. We show here that for every fixed k, B k -VPG \(\subsetneq\) B k + 1-VPG and that recognition of graphs from B k -VPG is NP-complete even when the input graph is given by a B k + 1-VPG representation. We also show that the class B k -VPG (for k ≥ 1) is in no inclusion relation with the class of intersection graphs of straight line segments in the plane.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Steven Chaplick
    • 1
  • Vít Jelínek
    • 2
  • Jan Kratochvíl
    • 3
  • Tomáš Vyskočil
    • 3
  1. 1.Department of MathematicsWilfrid Laurier UniversityWaterlooCanada
  2. 2.Computer Science Institute, Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic
  3. 3.Department of Applied Mathematics, Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic

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