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Gap-Planar Graphs

  • Sang Won Bae
  • Jean-Francois Baffier
  • Jinhee Chun
  • Peter Eades
  • Kord Eickmeyer
  • Luca Grilli
  • Seok-Hee Hong
  • Matias Korman
  • Fabrizio Montecchiani
  • Ignaz Rutter
  • Csaba D. Tóth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10692)

Abstract

We introduce the family of k-gap-planar graphs for \(k \ge 0\), i.e., graphs that have a drawing in which each crossing is assigned to one of the two involved edges and each edge is assigned at most k of its crossings. This definition finds motivation in edge casing, as a \(k\)-gap-planar graph can be drawn crossing-free after introducing at most k local gaps per edge. We obtain results on the maximum density, drawability of complete graphs, complexity of the recognition problem, and relationships with other families of beyond-planar graphs.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Sang Won Bae
    • 1
  • Jean-Francois Baffier
    • 2
  • Jinhee Chun
    • 3
  • Peter Eades
    • 4
  • Kord Eickmeyer
    • 5
  • Luca Grilli
    • 6
  • Seok-Hee Hong
    • 4
  • Matias Korman
    • 3
  • Fabrizio Montecchiani
    • 6
  • Ignaz Rutter
    • 7
  • Csaba D. Tóth
    • 8
  1. 1.Kyonggi UniversitySuwonSouth Korea
  2. 2.National Institute of InformaticsTokyoJapan
  3. 3.Tohoku UniversitySendaiJapan
  4. 4.University of SydneySydneyAustralia
  5. 5.TU DarmstadtDarmstadtGermany
  6. 6.University of PerugiaPerugiaItaly
  7. 7.TU EindhovenEindhovenThe Netherlands
  8. 8.California State University NorthridgeLos AngelesUSA

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