Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
SIAM Journal on Discrete Mathematics
On the crossing number of almost planar graphs
GD'06 Proceedings of the 14th international conference on Graph drawing
Approximating the Crossing Number of Apex Graphs
Graph Drawing
Approximating the crossing number of graphs embeddable in any orientable surface
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Do we really understand the crossing numbers?
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
A tighter insertion-based approximation of the crossing number
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Facets in the Crossing Number Polytope
SIAM Journal on Discrete Mathematics
Advances in the planarization method: effective multiple edge insertions
GD'11 Proceedings of the 19th international conference on Graph Drawing
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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 min-max formulas involving efficiently computable lower and upper bounds. These min-max results are the first of their kind in the study of crossing numbers and improve the approximation factor for the approximation algorithm given by Hliněný and Salazar (Graph Drawing GD 2006). On the other hand, we show that it is NP-hard to compute a weighted version of the crossing number for near-planar graphs.