Improved upper bounds on the crossing number
Proceedings of the twenty-fourth annual symposium on Computational geometry
Inserting a vertex into a planar graph
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Planar decompositions and the crossing number of graphs with an excluded minor
GD'06 Proceedings of the 14th international conference on Graph drawing
On the crossing number of almost planar graphs
GD'06 Proceedings of the 14th international conference on Graph drawing
Approximating the crossing number of toroidal graphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Algorithms for the hypergraph and the minor crossing number problems
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Do we really understand the crossing numbers?
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Crossing minimization and layouts of directed hypergraphs with port constraints
GD'10 Proceedings of the 18th international conference on Graph drawing
Crossing number additivity over edge cuts
European Journal of Combinatorics
Untangling graphs representing spatial relationships driven by drawing aesthetics
Proceedings of the 17th Panhellenic Conference on Informatics
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The minor crossing number of a graph G is defined as the minimum crossing number of all graphs that contain G as a minor. Basic properties of this new invariant are presented. We study topological structure of graphs with bounded minor crossing number and obtain a new strong version of a lower bound based on the genus. We also give a generalization of an inequality of Moreno and Salazar crossing numbers of a graph and its minors.