Circle-Representations of Simple 4-Regular Planar Graphs

Bekos, Michael A. and Raftopoulou, Chrysanthi N. (2013) Circle-Representations of Simple 4-Regular Planar Graphs. In: 20th International Symposium, GD 2012, September 19-21, 2012, Redmond, WA, USA , pp. 138-149 (Official URL: http://link.springer.com/chapter/10.1007/978-3-642-36763-2_13).

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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.

Item Type:Conference Paper
Additional Information:10.1007/978-3-642-36763-2_13
Classifications:P Styles > P.120 Circular
Z Theory > Z.250 Geometry
ID Code:1304

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