Results 51 to 60 of about 11,183,836 (302)
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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Genus, Treewidth, and Local Crossing Number
International Symposium Graph Drawing and Network Visualization, 2015 We consider relations between the size, treewidth, and local crossing number maximum number of crossings per edge of graphs embedded on topological surfaces.
V. Dujmović, D. Eppstein, D. Wood
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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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The Crossing Number of Cartesian Product of 5-Wheel with any Tree
Discussiones Mathematicae Graph Theory, 2021 In this paper, we establish the crossing number of join product of 5-wheel with n isolated vertices. In addition, the exact values for the crossing numbers of Cartesian products of the wheels of order at most five with any tree T are given.
Wang Yuxi, Huang Yuanqiu
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Crossing lemma for the odd-crossing number
Computational Geometry, 2023 A graph is $1$-planar, if it can be drawn in the plane such that there is at most one crossing on every edge. It is known, that $1$-planar graphs have at most $4n-8$ edges. We prove the following odd-even generalization. If a graph can be drawn in the plane such that every edge is crossed by at most one other edge {\em an odd number of times}, then it ...
Karl, János, Tóth, Géza
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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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The Crossing Numbers of Join of Some Graphs with n Isolated Vertices
Discussiones Mathematicae Graph Theory, 2018 There are only few results concerning crossing numbers of join of some graphs. In this paper, for some graphs on five vertices, we give the crossing numbers of its join with n isolated vertices.
Ding Zongpeng, Huang Yuanqiu
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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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Adding One Edge to Planar Graphs Makes Crossing Number and 1-Planarity Hard [PDF]
SIAM journal on computing (Print), 2012 A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show the surprising fact that it is NP-hard to compute the crossing number of near-planar graphs.
Sergio Cabello, B. Mohar
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Pediatric Blood &Cancer, EarlyView.Abstract Background Sickle cell disease (SCD) is an autosomal recessive hemoglobinopathy affecting millions of individuals worldwide. The clinical expression and psychosocial burden of SCD vary widely across geographical, cultural, and healthcare system contexts, underscoring the need for setting‐specific approaches to assessment.
Desiré Fantasia +7 more
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