Results 51 to 60 of about 1,312,414 (329)
Triple crossing number and double crossing braid index [PDF]
Journal of Knot Theory and Its Ramifications, 2019 Traditionally, knot theorists have considered projections of knots where there are two strands meeting at every crossing. A triple crossing is a crossing where three strands meet at a single point, such that each strand bisects the crossing. In this paper we find a relationship between the triple crossing number and the double crossing braid index for
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Monotone Crossing Number [PDF]
, 2012 The monotone crossing number of G is defined as the smallest number of crossing points in a drawing of G in the plane, where every edge is represented by an x-monotone curve, that is, by a connected continuous arc with the property that every vertical line intersects it in at most one point.
János Pach, Géza Tóth
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Exactly Solvable Lattice Models with Crossing Symmetry [PDF]
, 2012 We show how to compute the exact partition function for lattice statistical-mechanical models whose Boltzmann weights obey a special "crossing" symmetry.
Fendley, Paul, Simon, Steven H.
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Crossing Numbers of Periodic Graphs [PDF]
Journal of Graph Theory, 2015 AbstractA graph is periodic if it can be obtained by joining identical pieces in a cyclic fashion. It is shown that the limit crossing number of a periodic graph is computable. This answers a question of Richter [1, Problem 4.2].
Dvořák, Zdeněk, Mohar, Bojan
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On the Problems of
MathematicsA connected graph, G, is Crossing Free-connected (CF-connected) if there is a path between every pair of vertices with no crossing on its edges for each optimal drawing of G.
Michal Staš, Mária Timková
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A Note on the Crossing Numbers of 5-Regular Graphs
Discussiones Mathematicae Graph Theory, 2020 The crossing number cr(G) of a graph G is the smallest number of edge crossings in any drawing of G. In this paper, we prove that there exists a unique 5-regular graph G on 10 vertices with cr(G) = 2.
Ouyang Zhangdong
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New Bounds on Crossing Numbers [PDF]
Discrete & Computational Geometry, 1999 The notation \(f(n)\ll g(n)\) means that, as \(n\) goes to infinity, \(g(n)/f(n)\) goes to infinity also. For \(g\geq 0\), let \(S_g\) denote the closed orientable 2-manifold of genus \(g\), with \(\text{cr}_g(G)\) the minimum number of crossing points among all drawings of the graph \(G\) on \(S_g\).
Pach, J., Spencer, J., Tóth, G.
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Fixed parameter tractability of crossing minimization of almost-trees
, 2013 We investigate exact crossing minimization for graphs that differ from trees by a small number of additional edges, for several variants of the crossing minimization problem.
Bannister, Michael J. +2 more
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Sickle Cell Disease Is an Inherent Risk for Asthma in a Sibling Comparison Study
Pediatric Blood &Cancer, EarlyView.ABSTRACT Introduction Sickle cell disease (SCD) and asthma share a complex relationship. Although estimates vary, asthma prevalence in children with SCD is believed to be comparable to or higher than the general population. Determining whether SCD confers an increased risk for asthma remains challenging due to overlapping symptoms and the ...
Suhei C. Zuleta De Bernardis +9 more
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An Evolutionary Formulation of the Crossing Number Problem
Discrete Dynamics in Nature and Society, 2009 A graph drawing algorithm is presented which results in complete graphs having minimum crossings equal to that of Guy's conjecture. It is then generalized and formulated in an evolutionary algorithm (EA) to perform constrained search for the crossing ...
Che Sheng Gan +3 more
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