Results 251 to 260 of about 11,183,836 (302)

Crossing Number is NP-Complete

SIAM Journal on Algebraic Discrete Methods, 1983
The general crossing number decision problem is defined as follows: ''Given a graph G (multiple edges are allowed) and an integer k, is the crossing number of G less than or equal to k?'' The authors prove that the crossing number decision problem is NP-complete, and hence likely to be intractable.
Garey, M. R., Johnson, D. S.
openaire   +3 more sources

Parameterised Partially-Predrawn Crossing Number

International Symposium on Computational Geometry, 2022
Inspired by the increasingly popular research on extending partial graph drawings, we propose a new perspective on the traditional and arguably most important geometric graph parameter, the crossing number.
Thekla Hamm, Petr Hliněný
semanticscholar   +1 more source

On the 2-colored crossing number

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, R. Fabila-Monroy, Adrian Fuchs, C. Hidalgo-Toscano, I. Parada, B. Vogtenhuber, Francisco Zaragoza   +6 more
semanticscholar   +1 more source

Biplanar crossing numbers. II. Comparing crossing numbers and biplanar crossing numbers using the probabilistic method

Random Structures & Algorithms, 2008
AbstractThe biplanar crossing number cr2(G) of a graph G is min{cr(G1) + cr(G2)}, where cr is the planar crossing number. We show that cr2(G) ≤ (3/8)cr(G). Using this result recursively, we bound the thickness by Θ(G) ‐ 2 ≤ Kcr2(G)0.4057 log2n with some constant K.
Czabarka, Éva, Sýkora, Ondrej, Székely, László A., Vrťo, Imrich   +3 more
openaire   +2 more sources

Crossing Number for Graphs with Bounded Pathwidth

Algorithmica, 2016
The crossing number is the smallest number of pairwise edge crossings when drawing a graph into the plane. There are only very few graph classes for which the exact crossing number is known or for which there at least exist constant approximation ratios.
T. Biedl, Markus Chimani, Martin Derka, Petra Mutzel   +3 more
semanticscholar   +1 more source

Crossing Number is Hard for Kernelization

International Symposium on Computational Geometry, 2015
The graph crossing number problem, cr(G)
Petr Hliněný, Marek Dernár
semanticscholar   +1 more source

On Hardness of the Joint Crossing Number

International Symposium on Algorithms and Computation, 2015
The Joint Crossing Number problem asks for a simultaneous embedding of two disjoint graphs into one surface such that the number of edge crossings (between the two graphs) is minimized.
Petr Hliněný, G. Salazar
semanticscholar   +1 more source

Multi-crossing number for knots and the Kauffman bracket polynomial

Mathematical Proceedings of the Cambridge Philosophical Society, 2014
A multi-crossing (or n-crossing) is a singular point in a projection of a knot or link at which n strands cross so that each strand bisects the crossing.
C. Adams, Orsola Capovilla-Searle, Jesse Freeman, Daniel Irvine, Samantha Petti, Daniel Vítek, Ashley Weber, Sicong Zhang   +7 more
semanticscholar   +1 more source

Crossing Number Problems

The American Mathematical Monthly, 1973
(1973). Crossing Number Problems. The American Mathematical Monthly: Vol. 80, No. 1, pp. 52-58.
P. Erdos, R. K. Guy
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Ribbon crossing numbers, crossing numbers, and Alexander polynomials

Topology and its Applications, 2018
Ribbon \(2\)-knotted objects are locally flat embeddings of surfaces in \(4\)-space which bound immersed \(3\)-manifolds with only ribbon singularities. They appear as topological realizations of welded knotted objects, which is a natural quotient of virtual knot theory. Let \(K^2\) be a ribbon \(2\)-knot.
openaire   +1 more source