CircleRepresentations of Simple 4Regular Planar GraphsBekos, Michael A. and Raftopoulou, Chrysanthi N. (2013) CircleRepresentations of Simple 4Regular Planar Graphs. In: 20th International Symposium, GD 2012, September 1921, 2012 , pp. 138149(Official URL: http://link.springer.com/chapter/10.1007/9783642...). Full text not available from this repository.
Official URL: http://link.springer.com/chapter/10.1007/9783642...
AbstractLovász conjectured that every connected 4regular 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 3connected, and, (b) we demonstrate an infinite class of connected 4regular planar graphs which are not 3connected and do not admit a realization as a system of circles.
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