Results 1 to 10 of about 10,813,555 (336)
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. These objects are of use in phylogenetics and are represented with straight-line drawings where
Robin Anderson +10 more
semanticscholar +7 more sources
On the Pseudolinear Crossing Number [PDF]
Journal of 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 of a graph G is the minimum number of pairwise crossings of edges in a ...
César Hernández-Vélez +2 more
semanticscholar +7 more sources
Improvement on the Crossing Number of Crossing-Critical Graphs [PDF]
Discrete & Computational Geometry, 2020 The crossing number of a graph G is the minimum number of edge crossings over all drawings of G in the plane. A graph G is k -crossing-critical if its crossing number is at least k , but if we remove any edge of G , its crossing number drops below k ...
J'anos Bar'at, G'eza T'oth
semanticscholar +8 more sources
The Crossing Number of The Hexagonal Graph H3,n
Discussiones Mathematicae Graph Theory, 2019 In [C. Thomassen, Tilings of the torus and the Klein bottle and vertex-transitive graphs on a fixed surface, Trans. Amer. Math. Soc. 323 (1991) 605–635], Thomassen described completely all (except finitely many) regular tilings of the torus S1 and the ...
Wang Jing +2 more
doaj +2 more sources
The Bundled Crossing Number [PDF]
International Symposium Graph Drawing and Network Visualization, 2016 We study the algorithmic aspect of edge bundling. A bundled crossing in a drawing of a graph is a group of crossings between two sets of parallel edges. The bundled crossing number is the minimum number of bundled crossings that group all crossings in a ...
M. J. Alam, Martin Fink, S. Pupyrev
semanticscholar +5 more sources
Odd Crossing Number and Crossing Number Are Not the Same [PDF]
Discrete & Computational Geometry, 2008 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
openalex +5 more sources
Approximating the Rectilinear Crossing Number [PDF]
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.
J. Fox, J. Pach, Andrew Suk
semanticscholar +6 more sources
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
openalex +3 more sources
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
doaj +3 more sources
An Evolutionary Formulation of the Crossing Number Problem [PDF]
Discrete Dynamics in Nature and Society, 2009 A graph drawing algorithm is presented which results in complete graphs having minimum crossings equal to that of Guy's conjecture. It is then generalized and formulated in an evolutionary algorithm (EA) to perform constrained search for the crossing ...
Che Sheng Gan +3 more
doaj +2 more sources