Results 21 to 30 of about 308,302 (304)
On the Decay of Crossing Numbers [PDF]
Journal of Combinatorial Theory, Series B, 2007 Let \(\text{cr}(G)\) denote the crossing number of the graph \(G\). \textit{B. Richter} and \textit{C. Thomassen} [J. Comb. Theory, Ser. B 58, 217--224 (1993; Zbl 0733.05035)] conjectured that there is a constant \(c\) such that every graph \(G\) with crossing number \(k\) has an edge \(e\) such that \(\text{cr}(G-e)\geq k-c\sqrt{k}\), and showed that ...
Jacob Fox, Csaba D. Tóth
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Degenerate Crossing Numbers [PDF]
Discrete & Computational Geometry, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
János Pach, Géza Tóth 0001
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Parameterised Partially-Predrawn Crossing Number [PDF]
, 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.
Hliněný, Petr; orcid: +2 more
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Analogies between the Crossing Number and the Tangle Crossing Number [PDF]
The Electronic Journal of Combinatorics, 2018 Tanglegrams are special graphs that consist of a pair of rooted binary trees with the same number of leaves, and a perfect matching between the two leaf-sets. These objects are of use in phylogenetics and are represented with straight-line drawings where the leaves of the two plane binary trees are on two parallel lines and only the matching edges can ...
Robin Anderson +10 more
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On the Degenerate Crossing Number [PDF]
Discrete & Computational Geometry, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eyal Ackerman, Rom Pinchasi
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On the crossing number of join product of the discrete graph with special graphs of order five
Electronic Journal of Graph Theory and Applications, 2020 The main aim of the paper is to give the crossing number of join product G+Dn for the disconnected graph G of order five consisting of the complete graph K4 and of one isolated vertex.
Michal Staš
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The Crossing Number of Hexagonal Graph H3,n in the Projective Plane
Discussiones Mathematicae Graph Theory, 2022 Thomassen described all (except finitely many) regular tilings of the torus S1 and the Klein bottle N2 into (3,6)-tilings, (4,4)-tilings and (6,3)-tilings.
Wang Jing +3 more
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Crossing Numbers and Cutwidths [PDF]
Journal of Graph Algorithms and Applications, 2003 Summary: The crossing number of a graph \(G= (V, E)\), denoted by \(\text{cr}(G)\), is the smallest number of edge crossings in any drawing of \(G\) in the plane. We assume that the drawing is good, i.e., incident edges do not cross, two edges cross at most once and at most two edges cross in a point of the plane. \textit{F. T.
Hristo N. Djidjev, Imrich Vrto
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The Toroidal Crossing Number [PDF]
, 2011 Studying the crossing number of the complete bipartite graph K4,n in ...
Ling, Tang +2 more
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Plick Graphs with Crossing Number 1 [PDF]
, 2011 In this paper, we deduce a necessary and sufficient condition for graphs whose plick graphs have crossing number 1. We also obtain a necessary and sufficient condition for plick graphs to have crossing number 1 in terms of forbidden ...
Basavanagoud, B., Kulli, V.R.
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