Results 311 to 320 of about 10,813,555 (336)

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

Applications of the crossing number

Algorithmica, 1994
Keywords: 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, János Pach, Farhad Shahrokhi, Mario Szegedy   +3 more
openaire   +3 more sources

An ILP-based Proof System for the Crossing Number Problem

Embedded Systems and Applications, 2016
Formally, 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
semanticscholar   +1 more source

On the crossing number of the join of the discrete graph with one graph of order five

, 2017
The 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
semanticscholar   +1 more source

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

Crossing Number Problems

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
openaire   +2 more sources

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 bounds in knot mosaics

Journal of knot theory and its ramifications, 2014
Knot 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
semanticscholar   +1 more source

Ribbon crossing numbers, crossing numbers, and Alexander polynomials

Topology and its Applications, 2018
Abstract 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 )
openaire   +2 more sources