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ALGORITHMICA
2011
13 years 24 days ago
Crossing Number and Weighted Crossing Number of Near-Planar Graphs
A nonplanar graph G is near-planar if it contains an edge e such that G−e is planar. The problem of determining the crossing number of a near-planar graph is exhibited from diffe...
Sergio Cabello, Bojan Mohar
GD
2006
Springer
13 years 9 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
GD
2005
Springer
13 years 11 months ago
Odd Crossing Number Is Not Crossing Number
The crossing number of a graph is the minimum number of edge intersections in a plane drawing of a graph, where each intersection is counted separately. If instead we count the nu...
Michael J. Pelsmajer, Marcus Schaefer, Daniel Stef...
STOC
2001
ACM
143views Algorithms» more  STOC 2001»
14 years 6 months ago
Computing crossing numbers in quadratic time
We show that for every fixed ? there is a quadratic time algorithm that decides whether a given graph has crossing number at most and, if this is the case, computes a drawing of t...
Martin Grohe
GD
2008
Springer
13 years 6 months ago
Crossing and Weighted Crossing Number of Near-Planar Graphs
A nonplanar graph G is near-planar if it contains an edge e such that G − e is planar. The problem of determining the crossing number of a near-planar graph is exhibited from di...
Sergio Cabello, Bojan Mohar