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Intersection Dimension of Bipartite Graphs

  • Steven Chaplick
  • Pavol Hell
  • Yota Otachi
  • Toshiki Saitoh
  • Ryuhei Uehara
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8402)

Abstract

We introduce a concept of intersection dimension of a graph with respect to a graph class. This generalizes Ferrers dimension, boxicity, and poset dimension, and leads to interesting new problems. We focus in particular on bipartite graph classes defined as intersection graphs of two kinds of geometric objects. We relate well-known graph classes such as interval bigraphs, two-directional orthogonal ray graphs, chain graphs, and (unit) grid intersection graphs with respect to these dimensions. As an application of these graph-theoretic results, we show that the recognition problems for certain graph classes are NP-complete.

Keywords

Ferrers dimension Boxicity Unit grid intersection graph Segment-ray graphs Orthogonal ray graph NP-hardness 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Steven Chaplick
    • 1
  • Pavol Hell
    • 2
  • Yota Otachi
    • 3
  • Toshiki Saitoh
    • 4
  • Ryuhei Uehara
    • 3
  1. 1.Department of Applied Mathematics, Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic
  2. 2.School of Computing ScienceSimon Fraser UniversityBurnabyCanada
  3. 3.School of Information ScienceJapan Advanced Institute of Science and TechnologyNomiJapan
  4. 4.Graduate School of EngineeringKobe UniversityNadaJapan

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