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)


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.


Planar Graph Triangular Face Connected Planar Graph Contact Graph Tangent Circle 


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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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