Skip to main content
SpringerLink
Log in

On Edge Intersection Graphs of Paths with 2 Bends

  • Conference paper
  • First Online:
Book cover Graph-Theoretic Concepts in Computer Science (WG 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9941))

Included in the following conference series:

Abstract

An EPG-representation of a graph G is a collection of paths in a grid, each corresponding to a single vertex of G, so that two vertices are adjacent if and only if their corresponding paths share infinitely many points. In this paper we focus on graphs admitting EPG-representations by paths with at most 2 bends. We show hardness of the recognition problem for this class of graphs, along with some subclasses.

We also initiate the study of graphs representable by unaligned polylines, and by polylines, whose every segment is parallel to one of prescribed slopes. We show hardness of recognition and explore the trade-off between the number of bends and the number of slopes.

M. Pergel—Partially supported by a Czech research grant GAČR GA14-10799S.

P. Rzążewski—Supported by ERC Starting Grant PARAMTIGHT (No. 280152).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Booth, K., Lueker, G.: Testing for the consecutive ones property, interval graphs, and planarity using PQ-tree algorithms. J. Comput. Syst. Sci. 13, 335–389 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  2. Černý, J., Král, D., Nyklová, H., Pangrác, O.: On intersection graphs of segments with prescribed slopes. In: Mutzel, P., Jünger, M., Leipert, S. (eds.) GD 2001. LNCS, vol. 2265, pp. 261–271. Springer, Heidelberg (2002). doi:10.1007/3-540-45848-4_21

    Chapter  Google Scholar 

  3. Clark, B., Colbourn, C., Johnson, D.: Unit disk graphs. Disc. Math. 86, 165–177 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cameron, K., Chaplick, S., Hoang, C.T.: Edge intersection graphs of \(L\)-shaped paths in grids. Disc. Appl. Math. (2015, in press, available online)

    Google Scholar 

  5. Chaplick, S., Jelínek, V., Kratochvíl, J., Vyskočil, T.: Bend-bounded path intersection graphs: sausages, noodles, and waffles on a grill. In: Golumbic, M.C., Stern, M., Levy, A., Morgenstern, G. (eds.) WG 2012. LNCS, vol. 7551, pp. 274–285. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  6. Francis, M., Gonçalves, D., Ochem, P.: The maximum clique problem in multiple interval graphs. Algoritmica 71, 812–836 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  7. Golumbic, M., Lipshteyn, M., Stern, M.: Edge intersection graphs of single bend paths on a grid. Networks 54, 130–138 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Heldt, D., Knauer, K., Ueckerdt, T.: Edge-intersection graphs of grid paths: the bend-number. Disc. Appl. Math. 167, 144–162 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  9. Lovász, L: Coverings and coloring of hypergraphs. In: Proceedings of the 4th SEICCGTC, pp. 3–12 (1973)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Software and Computer Science Education, Charles University, Praha, Czech Republic

    Martin Pergel

  2. Institute of Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI), Budapest, Hungary

    Paweł Rzążewski

  3. Faculty of Mathematics and Information Science, Warsaw University of Technology, Warszawa, Poland

    Paweł Rzążewski

Authors
  1. Martin Pergel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paweł Rzążewski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paweł Rzążewski .

Editor information

Editors and Affiliations

  1. University of Bergen, Bergen, Norway

    Pinar Heggernes

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer-Verlag GmbH Germany

About this paper

Cite this paper

Pergel, M., Rzążewski, P. (2016). On Edge Intersection Graphs of Paths with 2 Bends. In: Heggernes, P. (eds) Graph-Theoretic Concepts in Computer Science. WG 2016. Lecture Notes in Computer Science(), vol 9941. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53536-3_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-53536-3_18

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53535-6

  • Online ISBN: 978-3-662-53536-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation