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ALGORITHMICA
2011

Crossing Number and Weighted Crossing Number of Near-Planar Graphs

8 years 5 months 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 different combinatorial viewpoints. On the one hand, we develop minmax formulas involving efficiently computable lower and upper bounds. These minmax results are the first of their kind in the study of crossing numbers and improve the approximation factor for the approximation algorithm given by Hlinˇený and Salazar (Graph Drawing GD’06). On the other hand, we show that it is NP-hard to compute a weighted version of the crossing number for near-planar graphs. Keywords Crossing number · Near-planar · Almost planar · Planar separation · Dual distance · Facial distance · NP-hardness
Sergio Cabello, Bojan Mohar
Added 12 May 2011
Updated 12 May 2011
Type Journal
Year 2011
Where ALGORITHMICA
Authors Sergio Cabello, Bojan Mohar
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