String graphs. II.: Recognizing string graphs is NP-hard
Journal of Combinatorial Theory Series B
Improved approximations of crossings in graph drawings
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Computing crossing numbers in quadratic time
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Crossing number is hard for cubic graphs
Journal of Combinatorial Theory Series B
Computing crossing number in linear time
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
The crossing number of K11 is 100
Journal of Graph Theory
A New Approach to Exact Crossing Minimization
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Approximating the Crossing Number of Apex Graphs
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
The complexity of several realizability problems for abstract topological graphs
GD'07 Proceedings of the 15th international conference on 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
Experiments on exact crossing minimization using column generation
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
GD'05 Proceedings of the 13th international conference on Graph Drawing
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
A branch-and-cut approach to the crossing number problem
Discrete Optimization
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In the last years, several integer linear programming (ILP) formulations for the crossing number problem arose. While they all contain a common conceptual core, the properties of the corresponding polytopes have never been investigated. In this paper, we formally establish the crossing number polytope and show several facet-defining constraint classes.