Chapter

Graph Drawing

Volume 8242 of the series Lecture Notes in Computer Science pp 71-82

A Linear-Time Algorithm for Testing Outer-1-Planarity

  • Seok-Hee HongAffiliated withUniversity of Sydney
  • , Peter EadesAffiliated withUniversity of Sydney
  • , Naoki KatohAffiliated withKyoto University
  • , Giuseppe LiottaAffiliated withUniversity of Perugia
  • , Pascal SchweitzerAffiliated withETH
  • , Yusuke SuzukiAffiliated withNiigata University

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Abstract

A graph is 1-planar if it can be embedded in the plane with at most one crossing per edge. A graph is outer-1-planar if it has an embedding in which every vertex is on the outer face and each edge has at most one crossing. We present a linear time algorithm to test whether a graph is outer-1-planar. The algorithm can be used to produce an outer-1-planar embedding in linear time if it exists.