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Re-embedding a 1-Plane Graph into a Straight-Line Drawing in Linear Time

  • Seok-Hee Hong
  • Hiroshi Nagamochi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9801)

Abstract

Thomassen characterized some 1-plane embedding as the forbidden configuration such that a given 1-plane embedding of a graph is drawable in straight-lines if and only if it does not contain the configuration [C. Thomassen, Rectilinear drawings of graphs, J. Graph Theory, 10(3), 335–341, 1988].

In this paper, we characterize some 1-plane embedding as the forbidden configuration such that a given 1-plane embedding of a graph can be re-embedded into a straight-line drawable 1-plane embedding of the same graph if and only if it does not contain the configuration. Re-embedding of a 1-plane embedding preserves the same set of pairs of crossing edges. We give a linear-time algorithm for finding a straight-line drawable 1-plane re-embedding or the forbidden configuration.

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.University of SydneySydneyAustralia
  2. 2.Kyoto UniversityKyotoJapan

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