Graphs that admit polyline drawings with few crossing angles

Eyal Ackerman, Radoslav Fulek, Csaba D. Tóth

Research output: Contribution to journalArticlepeer-review


We consider graphs that admit polyline drawings where all crossings occur at the same angle a ε (0, φ 2 ]. We prove that every graph on n vertices that admits such a polyline drawing with at most two bends per edge has O(n) edges. This result remains true when each crossing occurs at an angle from a small set of angles. We also provide several extensions that might be of independent interest.

Original languageEnglish
Pages (from-to)305-320
Number of pages16
JournalSIAM Journal on Discrete Mathematics
Issue number1
StatePublished - 2012


  • Crossing number
  • Geometric graph
  • Polyline drawing

ASJC Scopus subject areas

  • General Mathematics


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