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Hanani-Tutte and Monotone Drawings

  • Radoslav Fulek
  • Michael J. Pelsmajer
  • Marcus Schaefer
  • Daniel Štefankovič
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6986)

Abstract

A drawing of a graph is x-monotone if every edge intersects every vertical line at most once and every vertical line contains at most one vertex. Pach and Tóth showed that if a graph has an x-monotone drawing in which every pair of edges crosses an even number of times, then the graph has an x-monotone embedding in which the x-coordinates of all vertices are unchanged. We give a new proof of this result and strengthen it by showing that the conclusion remains true even if adjacent edges are allowed to cross oddly. This answers a question posed by Pach and Tóth. Moreover, we show that an extension of this result for graphs with non-adjacent pairs of edges crossing oddly fails even if there exists only one such pair in a graph.

Keywords

Planar Graph Rotation System Swiss National Science Foundation Interior Vertex Independent Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Radoslav Fulek
    • 1
  • Michael J. Pelsmajer
    • 2
  • Marcus Schaefer
    • 3
  • Daniel Štefankovič
    • 4
  1. 1.Ecole Polytechnique Fédérale de LausanneLausanneSwitzerland
  2. 2.Illinois Institute of TechnologyChicagoUSA
  3. 3.DePaul UniversityChicagoUSA
  4. 4.University of RochesterRochesterUSA

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