A separator theorem for graphs of bounded genus
Journal of Algorithms
Edge separators for graphs of bounded genus with applications
Theoretical Computer Science
On VLSI layouts of the star graph and related networks
Integration, the VLSI Journal
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Improved Approximations of Crossings in Graph Drawings and VLSI Layout Areas
SIAM Journal on Computing
Algorithms for the fixed linear crossing number problem
Discrete Applied Mathematics
Planarization of Graphs Embedded on Surfaces
WG '95 Proceedings of the 21st International Workshop on Graph-Theoretic Concepts in Computer Science
The crossing number of Cm × Cn is as conjectured for n ≥ m(m + 1)
Journal of Graph Theory
GD'05 Proceedings of the 13th international conference on Graph Drawing
Crossing number of toroidal graphs
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
Planar decompositions and the crossing number of graphs with an excluded minor
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
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
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Pach and Tóth [14] proved that any n-vertex graph of genus g and maximum degree d has a planar crossing number at most cgdn, for a constant c 1. We improve on this results by decreasing the bound to O(dgn), if g = o(n), and to O(g2), otherwise, and also prove that our result is tight within a constant factor.