Results 11 to 20 of about 10,813,555 (336)
On the Maximum Crossing Number
Journal of Graph Algorithms and Applications, 2018 Research about crossings is typically about minimization. In this paper, we consider maximizing the number of crossings over all possible ways to draw a given graph in the plane. Alpert et al. [Electron. J. Combin., 2009] conjectured that any graph has a convex straight-line drawing, that is, a drawing with vertices in convex position ...
Markus Chimani +5 more
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On the 2-colored crossing number [PDF]
International Symposium Graph Drawing and Network Visualization, 2019 Let $D$ be a straight-line drawing of a graph. The rectilinear 2-colored crossing number of $D$ is the minimum number of crossings between edges of the same color, taken over all possible 2-colorings of the edges of $D$.
O. Aichholzer +6 more
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Note on the Pair-crossing Number and the Odd-crossing Number [PDF]
Discrete & Computational Geometry, 2007 The crossing number ${\mbox{\sc cr}}(G)$ of a graph G is the minimum possible number of edge-crossings in a drawing of G, the pair-crossing number ${\mbox{\sc pair-cr}}(G)$ is the minimum possible number of crossing pairs of edges in a drawing of G, and the odd-crossing number ${\mbox{\sc odd-cr}}(G)$ is the minimum number of pairs of edges that cross ...
Gézá Tóth
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Hardness of Approximation for Crossing Number [PDF]
Discrete & Computational Geometry, 2012 We show that, if $\mathrm{P}\not=\mathrm{NP}$, there is a constant c0>1 such that there is no c0-approximation algorithm for the crossing number, even when restricted to 3-regular graphs.
Sergio Cabello
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Implementation of Minutiae Based Fingerprint Identification System Using Crossing Number Concept [PDF]
Informatică economică, 2014 Biometric system is essentially a pattern recognition system which recognizes a person by determining the authenticity of a specific physiological (e.g., fingerprints, face, retina, iris) or behavioral (e.g., gait, signature) characteristic possessed by ...
Atul S. CHAUDHARI +2 more
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On the Degenerate Crossing Number [PDF]
Discrete & Computational Geometry, 2013 The degenerate crossing number\({\text{ cr}^{*}}(G)\) of a graph \(G\) is the minimum number of crossing points of edges in any drawing of \(G\) as a simple topological graph in the plane. This notion was introduced by Pach and Toth who showed that for a graph \(G\) with \(n\) vertices and \(e \ge 4n\) edges \({\text{ cr}^{*}}(G)=\Omega \big (e^4 / n^4\
Eyal Ackerman, R. Pinchasi
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Cubicity, degeneracy, and crossing number
European Journal of Combinatorics, 2013 21 ...
Abhijin Adiga +2 more
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Effect of a crossing change on crossing number
, 2011 11 pages, 12 ...
Longting Wu +3 more
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A subpolynomial approximation algorithm for graph crossing number in low-degree graphs [PDF]
Symposium on the Theory of Computing, 2022 We consider the classical Minimum Crossing Number problem: given an n-vertex graph G, compute a drawing of G in the plane, while minimizing the number of crossings between the images of its edges.
Julia Chuzhoy, Zihan Tan
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The average genus of oriented rational links with a given crossing number [PDF]
Journal of knot theory and its ramifications, 2022 . In this paper, we enumerate the number of oriented rational knots and the number of oriented rational links with any given crossing number and minimum genus.
Dawn Ray, Y. Diao
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