Results 11 to 20 of about 9,538,132 (298)
Minor-monotone crossing number [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 The minor crossing number of a graph $G$, $rmmcr(G)$, is defined as the minimum crossing number of all graphs that contain $G$ as a minor. We present some basic properties of this new minor-monotone graph invariant.
Drago Bokal +2 more
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Odd crossing number is not crossing number [PDF]
, 2005 The crossing number of a graph is the minimum number of edge intersections in a plane drawing of a graph, where each intersection is counted separately. If instead we count the number of pairs of edges that intersect an odd number of times, we obtain the
Daniel Stefankovič +6 more
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Odd Crossing Number and Crossing Number Are Not the Same [PDF]
Discrete & Computational Geometry, 2006 The crossing number of a graph is the minimum number of edge intersections in aplane drawing of a graph, where each intersection is counted separately. If instead we count the number of pairs of edges that intersect an odd number of times, we obtainthe ...
Marcus Schaefer, Daniel Stefankovič +1 more
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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 4 pi - 8 edges. We prove the following odd-even generalization.
Tóth, Géza +3 more
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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 ...
János Pach +3 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.
Markus Chimani +5 more
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Approximating the Bundled Crossing Number
Journal of Graph Algorithms and Applications, 2023 Bundling crossings is a strategy which can enhance the readability of graph drawings. In this paper we consider good drawings, i.e., we require that any two edges have at most one common point which can be a common vertex or a crossing.
Alan Arroyo, Stefan Felsner
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Crossing Number, Pair-Crossing Number, and Expansion
Journal of Combinatorial Theory, Series B, 2004 The crossing number cr(G) of a graph G is the minimum possible number of edge crossings in a drawing of G in the plane, while the pair-crossing number pcr(G), introduced by Pach and Toth, is the smallest number of pairs of edges that cross in a drawing
Jiri Matousek, Petr Kolman
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Which Crossing Number is It, Anyway?
Journal of Combinatorial Theory, Series B, 2007 A drawing of a graph G is a mapping which assigns to each vertex a point of the plane and to each edge a simple continuous arc connecting the corresponding two points. The crossing number of G is the minimum number of crossing points in any drawing of G.
János Pach +3 more
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On the pseudolinear crossing number
J. Graph Theory, 2014 A drawing of a graph is pseudolinear if there is a pseudoline arrangement such that each pseudoline contains exactly one edge of the drawing. The pseudolinear crossing number c̃r(G) of a graph G is the minimum number of pairwise crossings of edges in a ...
Gelasio Salazar +2 more
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