Results 11 to 20 of about 307,259 (304)
Odd Crossing Number Is Not Crossing Number [PDF]
, 2006 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 odd crossing number. We show that there is a graph for which these two concepts differ, answering a
Michael J. Pelsmajer +2 more
openaire +2 more sources
The Bundled Crossing Number [PDF]
, 2016 Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016)
Alam, M. J., Fink, M., Pupyrev, S.
core +6 more sources
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
openaire +5 more sources
Crossing number, pair-crossing number, and expansion
Journal of Combinatorial Theory, Series B, 2004 The crossing number \(\text{cr}(G)\) of a graph \(G\) is the minimum possible number of edge crossings in a drawing of \(G\) in the plane, and the pair-crossing number \( \text{pcr}(G)\) of a graph \(G\) is smallest number of pairs of crossing edges in any drawing of \(G\) in the plane.
Petr Kolman, Jirí Matousek 0001
openaire +2 more sources
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 line intersects it in at most one point.
János Pach, Géza Tóth 0001
openaire +2 more sources
On the pseudolinear crossing number
J. Graph Theory, 2014 A drawing of a graph is {\em pseudolinear} if there is a pseudoline arrangement such that each pseudoline contains exactly one edge of the drawing. The {\em pseudolinear crossing number} of a graph $G$ is the minimum number of pairwise crossings of edges in a pseudolinear drawing of $G$.
César Hernández-Vélez +2 more
openaire +4 more sources
Which Crossing Number Is It Anyway?
Journal of Combinatorial Theory, Series B, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
János Pach, Géza Tóth 0001
core +3 more sources
Approximating the rectilinear crossing number
Computational Geometry, 2016 A straight-line drawing of a graph $G$ is a mapping which assigns to each vertex a point in the plane and to each edge a straight-line segment connecting the corresponding two points. The rectilinear crossing number of a graph $G$, $\overline{cr}(G)$, is the minimum number of crossing edges in any straight-line drawing of $G$. Determining or estimating
Fox, Jacob, Pach, János, Suk, Andrew
openaire +6 more sources
Complexity of Anchored Crossing Number and Crossing Number of Almost Planar Graphs
CoRR, 2023 In this paper we deal with the problem of computing the exact crossing number of almost planar graphs and the closely related problem of computing the exact anchored crossing number of a pair of planar graphs. It was shown by [Cabello and Mohar, 2013] that both problems are NP-hard; although they required an unbounded number of high-degree vertices (in
Hliněný, Petr
openaire +4 more sources
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
core +1 more source