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» Obfuscated Drawings of Planar Graphs
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COMPGEOM
2010
ACM
14 years 2 months 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
ESA
2008
Springer
130views Algorithms» more  ESA 2008»
13 years 11 months ago
Linear Time Planarity Testing and Embedding of Strongly Connected Cyclic Level Graphs
Abstract. A level graph is a directed acyclic graph with a level assignment for each node. Such graphs play a prominent role in graph drawing. They express strict dependencies and ...
Christian Bachmaier, Wolfgang Brunner
GD
2006
Springer
14 years 1 months ago
Planar Decompositions and the Crossing Number of Graphs with an Excluded Minor
Tree decompositions of graphs are of fundamental importance in structural and algorithmic graph theory. Planar decompositions generalise tree decompositions by allowing an arbitrar...
David R. Wood, Jan Arne Telle
COMGEO
2011
ACM
13 years 4 months ago
Characterizations of restricted pairs of planar graphs allowing simultaneous embedding with fixed edges
A set of planar graphs share a simultaneous embedding if they can be drawn on the same vertex set V in the Euclidean plane without crossings between edges of the same graph. Fixed ...
J. Joseph Fowler, Michael Jünger, Stephen G. ...
GD
2009
Springer
14 years 2 months ago
Leftist Canonical Ordering
Canonical ordering is an important tool in planar graph drawing and other applications. Although a linear-time algorithm to determine canonical orderings has been known for a while...
Melanie Badent, Michael Baur, Ulrik Brandes, Sabin...