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. © 2013 Springer-Verlag.
CITATION STYLE
Bekos, M. A., & Raftopoulou, C. N. (2013). Circle-representations of simple 4-regular planar graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7704 LNCS, pp. 138–149). https://doi.org/10.1007/978-3-642-36763-2_13
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