Results 311 to 320 of about 10,813,555 (336)
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Parameterised Partially-Predrawn Crossing Number
International Symposium on Computational Geometry, 2022Inspired 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
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Applications of the crossing number
Algorithmica, 1994Keywords: crossing number ; bisection width of a graph Note: Professor Pach's number: [105]. Also in: Proc. 10th ACM Symposium on Computational Geometry, 1994, 198-202.
János Pach+3 more
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An ILP-based Proof System for the Crossing Number Problem
Embedded Systems and Applications, 2016Formally, approaches based on mathematical programming are able to find provably optimal solutions. However, the demands on a verifiable formal proof are typically much higher than the guarantees we can sensibly attribute to implementations of ...
Markus Chimani, Tilo Wiedera
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On the crossing number of the join of the discrete graph with one graph of order five
, 2017The crossing number cr(G) of a graph G is the minimal number of edge crossings over all drawings of G in the plane. In the paper, we extend results of the exact values of crossing numbers for join of graphs of order five.
M. Staš
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Crossing Number for Graphs with Bounded Pathwidth
Algorithmica, 2016The 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+3 more
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Crossing Number is Hard for Kernelization
International Symposium on Computational Geometry, 2015The graph crossing number problem, cr(G)
Petr Hliněný, Marek Dernár
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The American Mathematical Monthly, 1973
(1973). Crossing Number Problems. The American Mathematical Monthly: Vol. 80, No. 1, pp. 52-58.
Richard K. Guy, Paul Erdös
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(1973). Crossing Number Problems. The American Mathematical Monthly: Vol. 80, No. 1, pp. 52-58.
Richard K. Guy, Paul Erdös
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Multi-crossing number for knots and the Kauffman bracket polynomial
Mathematical Proceedings of the Cambridge Philosophical Society, 2014A 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+7 more
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Crossing number bounds in knot mosaics
Journal of knot theory and its ramifications, 2014Knot mosaics are used to model physical quantum states. The mosaic number of a knot is the smallest integer [Formula: see text] such that the knot can be represented as a knot [Formula: see text]-mosaic. In this paper, we establish an upper bound for the
H. Howards, Andrew Kobin
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Ribbon crossing numbers, crossing numbers, and Alexander polynomials
Topology and its Applications, 2018Abstract A 2-knot is a surface in R 4 that is homeomorphic to S 2 , the standard sphere in 3-space. A ribbon 2-knot is a 2-knot obtained from m 2-spheres in R 4 by connecting them with m − 1 annuli. Let K 2 be a ribbon 2-knot. The ribbon crossing number, denoted by r- c r ( K 2 )
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