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

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


We introduce the family of k-gap-planar graphs for k≥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 is motivated by applications in edge casing, as a k-gap-planar graph can be drawn crossing-free after introducing at most k local gaps per edge. We present results on the maximum density of k-gap-planar graphs, their relationship to other classes of beyond-planar graphs, characterization of k-gap-planar complete graphs, and the computational complexity of recognizing k-gap-planar graphs.

Original languageEnglish
Pages (from-to)36-52
Number of pages17
JournalTheoretical Computer Science
Publication statusPublished - 2018 Oct 12


  • Beyond planarity k-gap-planar graphs
  • Complete graphs
  • Density results
  • Recognition problem
  • k-planar graphs
  • k-quasiplanar graphs


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