Results 11 to 20 of about 1,312,414 (329)
Analogies between the crossing number and the tangle crossing number [PDF]
The Electronic Journal of Combinatorics, 2017 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.
Anderson, Robin +10 more
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On the Maximum Crossing Number
Journal of Graph Algorithms and Applications, 2017 Research about crossings is typically about minimization. In this paper, we consider \emph{maximizing} the number of crossings over all possible ways to draw a given graph in the plane. Alpert et al. [Electron. J.
E Steinitz +18 more
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Crossing lemma for the odd-crossing number [PDF]
Computational Geometry, 2022 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 ...
János Karl, Gézá Tóth
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Cubicity, Degeneracy, and Crossing Number
European Journal of Combinatorics, 2011 21 ...
Abhijin Adiga +2 more
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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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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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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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On the crossing numbers of join products of W_{4}+P_{n} and W_{4}+C_{n} [PDF]
Opuscula Mathematica, 2021 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 the paper is to give the crossing number of the join product \(W_4+P_n\) and \(W_4+C_n\) for the ...
Michal Staš, Juraj Valiska
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Odd Crossing Number and Crossing Number Are Not the Same [PDF]
Discrete & Computational Geometry, 2006 The crossing number \(\text{cr}(G)\) of a graph \(G\) is the minimum number of edge crossings, taken over all drawing of \(G\) in the plane. Similarly \(\text{per}(G)\) (respectively \(\text{ocr}(G)\)) denotes the minimum number of pairs of edges which cross at least once (respectively an odd number of times), over all drawings of \(G\) in the plane ...
Pelsmajer, Michael J. +2 more
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