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» Crossing and Weighted Crossing Number of Near-Planar Graphs
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GD
2005
Springer
13 years 11 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...
JGT
2010
113views more  JGT 2010»
13 years 4 months ago
Crossing numbers of imbalanced graphs
The crossing number, cr(G), of a graph G is the least number of crossing points in any drawing of G in the plane. According to the Crossing Lemma of Ajtai, Chv´atal, Newborn, Sze...
János Pach, József Solymosi, G&aacut...
STOC
2001
ACM
143views Algorithms» more  STOC 2001»
14 years 6 months ago
Computing crossing numbers in quadratic time
We show that for every fixed ? there is a quadratic time algorithm that decides whether a given graph has crossing number at most and, if this is the case, computes a drawing of t...
Martin Grohe
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
WEA
2007
Springer
112views Algorithms» more  WEA 2007»
14 years 10 days ago
Crossing Minimization in Weighted Bipartite Graphs
Given a bipartite graph G = (L0, L1, E) and a fixed ordering of the nodes in L0, the problem of finding an ordering of the nodes in L1 that minimizes the number of crossings has ...
Olca A. Çakiroglu, Cesim Erten, Ömer K...