Results 11 to 20 of about 1,321,651 (326)
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 Maximum Crossing Number
Journal of Graph Algorithms and Applications, 2018 Research about crossings is typically about minimization. In this paper, we consider maximizing the number of crossings over all possible ways to draw a given graph in the plane. Alpert et al. [Electron. J. Combin., 2009] conjectured that any graph has a convex straight-line drawing, that is, a drawing with vertices in convex position ...
Markus Chimani +5 more
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The crossing numbers of join products of paths with three graphs of order five [PDF]
Opuscula Mathematica, 2022 The main aim of this paper is to give the crossing number of the join product \(G^\ast+P_n\) for the disconnected graph \(G^\ast\) of order five consisting of the complete graph \(K_4\) and one isolated vertex, where \(P_n\) is the path on \(n\) vertices.
Michal Staš, Mária Švecová
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The crossing numbers of join products of eight graphs of order six with paths and cycles
Karpatsʹkì Matematičnì Publìkacìï, 2023 The crossing number $\mathrm{cr}(G)$ of a graph $G$ is the minimum number of edge crossings over all drawings of $G$ in the plane. The main aim of this paper is to give the crossing numbers of the join products of eight graphs on six vertices with paths ...
M. Staš
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Degenerate Crossing Numbers [PDF]
Discrete & Computational Geometry, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pach, János, Tóth, Géza
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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.
Djidjev, Hristo N., Vrt'o, Imrich
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Skewness and the crossing numbers of graphs
AIMS Mathematics, 2023 The skewness of a graph $ G $, $ sk(G) $, is the smallest number of edges that need to be removed from $ G $ to make it planar. The crossing number of a graph $ G $, $ cr(G) $, is the minimum number of crossings over all possible drawings of $ G $. There
Zongpeng Ding
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Software Solution of the Algorithm of the Cyclic-Order Graph [PDF]
Acta Electrotechnica et Informatica, 2018 In this paper we describe by pseudo-code the ``Algorithm of the cyclic-order graph'', which we programmed in MATLAB 2016a and which is also possible to be executed in GNU Octave. We describe program's functionality and its use.
Štefan Berežný +2 more
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On the crossing number for Kronecker product of a tripartite graph with path
AKCE International Journal of Graphs and Combinatorics, 2020 The crossing number of a graph G, Cr(G) is the minimum number of edge crossings overall good drawings of G. Among the well-known four standard graph products namely Cartesian product, Kronecker product, strong product and lexicographic product, the one ...
N. Shanthini, J. Baskar Babujee
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Cyclic Permutations in Determining Crossing Numbers
Discussiones Mathematicae Graph Theory, 2022 The crossing number of a graph G is the minimum number of edge crossings over all drawings of G in the plane. Recently, the crossing numbers of join products of two graphs have been studied.
Klešč Marián, Staš Michal
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