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» On the Decay of Crossing Numbers
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GD
2005
Springer
13 years 10 months ago
Odd Crossing Number Is Not Crossing Number
The crossing number of a graph is the minimum number of edge intersections in a plane drawing of a graph, where each intersection is counted separately. If instead we count the nu...
Michael J. Pelsmajer, Marcus Schaefer, Daniel Stef...
ALGORITHMICA
2011
13 years 10 days ago
Crossing Number 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 diffe...
Sergio Cabello, Bojan Mohar
GD
2006
Springer
13 years 9 months ago
Planar Decompositions and the Crossing Number of Graphs with an Excluded Minor
Tree decompositions of graphs are of fundamental importance in structural and algorithmic graph theory. Planar decompositions generalise tree decompositions by allowing an arbitrar...
David R. Wood, Jan Arne Telle
CORR
2000
Springer
71views Education» more  CORR 2000»
13 years 5 months ago
Smoothness and decay properties of the limiting Quicksort density function
Using Fourier analysis, we prove that the limiting distribution of the standardized random number of comparisons used by Quicksort to sort an array of n numbers has an everywhere ...
James Allen Fill, Svante Janson