On embedding a graph in the grid with the minimum number of bends
SIAM Journal on Computing
Generating all 3-connected 4-regular planar graphs from the octahedron graph
Journal of Graph Theory
Classes and recognition of curve contact graphs
Journal of Combinatorial Theory Series B
Representing graphs by disks and balls (a survey of recognition-complexity results)
Discrete Mathematics
A Better Heuristic for Orthogonal Graph Drawings
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
New lower bound techniques for VLSI
SFCS '81 Proceedings of the 22nd Annual Symposium on Foundations of Computer Science
Universality considerations in VLSI circuits
IEEE Transactions on Computers
Drawing trees with perfect angular resolution and polynomial area
GD'10 Proceedings of the 18th international conference on Graph drawing
Force-Directed lombardi-style graph drawing
GD'11 Proceedings of the 19th international conference on Graph Drawing
Hi-index | 0.00 |
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.