Journal of Graph Theory
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Which Crossing Number is it, Anyway?
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Computing crossing numbers in quadratic time
Journal of Computer and System Sciences - STOC 2001
The crossing number of Cm × Cn is as conjectured for n ≥ m(m + 1)
Journal of Graph Theory
Odd crossing number is not crossing number
GD'05 Proceedings of the 13th international conference on Graph Drawing
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
On the Red/Blue Spanning Tree Problem
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
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
Crossing number of graphs with rotation systems
GD'07 Proceedings of the 15th international conference on Graph drawing
Adding one edge to planar graphs makes crossing number hard
Proceedings of the twenty-sixth annual symposium on Computational geometry
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
On the red/blue spanning tree problem
Theoretical Computer Science
An algorithm for the graph crossing number problem
Proceedings of the forty-third annual ACM symposium on Theory of computing
Facets in the Crossing Number Polytope
SIAM Journal on Discrete Mathematics
Orthogonal drawings and crossing numbers of the Kronecker product of two cycles
Journal of Parallel and Distributed Computing
On graph crossing number and edge planarization
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Complexity of some geometric and topological problems
GD'09 Proceedings of the 17th international conference on Graph Drawing
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It was proved by [M.R. Garey, D.S. Johnson, Crossing number is NP-complete, SIAM J. Algebraic Discrete Methods 4 (1983) 312-316] that computing the crossing number of a graph is an NP-hard problem. Their reduction, however, used parallel edges and vertices of very high degrees. We prove here that it is NP-hard to determine the crossing number of a simple 3-connected cubic graph. In particular, this implies that the minor-monotone version of the crossing number problem is also NP-hard, which has been open till now.