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» General Lower Bounds for the Minor Crossing Number of Graphs

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SIAMDM
2010

170views more SIAMDM 2010»

Complete Minors and Independence Number

13 years 3 days ago

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Let G be a graph with n vertices and independence number . Hadwiger's conjecture implies that G contains a clique minor of order at least n/. In 1982, Duchet and Meyniel prov...

Jacob Fox

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ALGORITHMICA
2011

198views Artificial Intelligence» more ALGORITHMICA 2011»

Crossing Number and Weighted Crossing Number of Near-Planar Graphs

13 years 12 days ago

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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 diffe...

Sergio Cabello, Bojan Mohar

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SODA
2010
ACM

248views Algorithms» more SODA 2010»

Approximating the Crossing Number of Graphs Embeddable in Any Orientable Surface

14 years 2 months ago

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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

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ENDM
2008

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A central approach to bound the number of crossings in a generalized configuration

13 years 5 months ago

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A generalized configuration is a set of n points and n 2 pseudolines such that each pseudoline passes through exactly two points, two pseudolines intersect exactly once, and no th...

Bernardo M. Ábrego, Silvia Fernández...

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DCG
2006

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k-Sets, Convex Quadrilaterals, and the Rectilinear Crossing Number of Kn

13 years 5 months ago