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GD
2006
Springer
13 years 11 months ago
Simultaneous Graph Embedding with Bends and Circular Arcs
Abstract. We consider the problem of simultaneous embedding of planar graphs. We demonstrate how to simultaneously embed a path and an n-level planar graph and how to use radial em...
Justin Cappos, Alejandro Estrella-Balderrama, J. J...
COMPGEOM
2010
ACM
14 years 23 days ago
Adding one edge to planar graphs makes crossing number hard
A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show that it is NP-hard to compute the crossing number of near-planar graphs. The main idea ...
Sergio Cabello, Bojan Mohar
JGT
2008
74views more  JGT 2008»
13 years 7 months ago
Straight line embeddings of cubic planar graphs with integer edge lengths
We prove that every simple cubic planar graph admits a planar embedding such that each edge is embedded as a straight line segment of integer length.
Jim Geelen, Anjie Guo, David McKinnon
JCT
2006
134views more  JCT 2006»
13 years 7 months ago
MacLane's planarity criterion for locally finite graphs
MacLane's planarity criterion states that a finite graph is planar if and only if its cycle space has a basis B such that every edge is contained in at most two members of B....
Henning Bruhn, Maya Jakobine Stein
COCO
2007
Springer
87views Algorithms» more  COCO 2007»
14 years 1 months ago
Parity Problems in Planar Graphs
We consider the problem of counting the number of spanning trees in planar graphs. We prove tight bounds on the complexity of the problem, both in general and especially in the mo...
Mark Braverman, Raghav Kulkarni, Sambuddha Roy