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» Odd Crossing Number Is Not Crossing Number
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MFCS
2004
Springer
13 years 11 months ago
Crossing Number Is Hard for Cubic Graphs
It was proved by [Garey and Johnson, 1983] that computing the crossing number of a graph is an NP-hard problem. Their reduction, however, used parallel edges and vertices of very h...
Petr Hlinený
GD
2008
Springer
13 years 7 months ago
Crossing and Weighted Crossing Number of Near-Planar Graphs
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 di...
Sergio Cabello, Bojan Mohar
SODA
2010
ACM
248views Algorithms» more  SODA 2010»
14 years 3 months ago
Approximating the Crossing Number of Graphs Embeddable in Any Orientable Surface
The crossing number of a graph is the least number of pairwise edge crossings in a drawing of the graph in the plane. We provide an O(n log n) time constant factor approximation al...
Petr Hlineny, Markus Chimani
CORR
2010
Springer
103views Education» more  CORR 2010»
13 years 6 months ago
On Graph Crossing Number and Edge Planarization
Given an n-vertex graph G, a drawing of G in the plane is a mapping of its vertices into points of the plane, and its edges into continuous curves, connecting the images of their ...
Julia Chuzhoy, Yury Makarychev, Anastasios Sidirop...
ENDM
2008
81views more  ENDM 2008»
13 years 6 months ago
The maximum number of halving lines and the rectilinear crossing number of Kn for n
For n 27 we present exact values for the maximum number h(n) of halving lines and h(n) of halving pseudolines, determined by n points in the plane. For this range of values of n ...
Bernardo M. Ábrego, Silvia Fernández...