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Circle-Representations of Simple 4-Regular Planar Graphs

  • Michael A. Bekos
  • Chrysanthi N. Raftopoulou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7704)

Abstract

Lovász conjectured that every connected 4-regular planar graph G admits a realization as a system of circles, i.e., it can be drawn on the plane utilizing a set of circles, such that the vertices of G correspond to the intersection and touching points of the circles and the edges of G are the arc segments among pairs of intersection and touching points of the circles. In this paper, (a) we affirmatively answer Lovász’s conjecture, if G is 3-connected, and, (b) we demonstrate an infinite class of connected 4-regular planar graphs which are not 3-connected and do not admit a realization as a system of circles.

Keywords

Planar Graph Triangular Face Connected Planar Graph Contact Graph Tangent Circle 
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 2013

Authors and Affiliations

  • Michael A. Bekos
    • 1
  • Chrysanthi N. Raftopoulou
    • 2
  1. 1.Institute for InformaticsUniversity of TübingenGermany
  2. 2.School of Applied Mathematical & Physical SciencesNational Technical University of AthensGreece

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