Browsing by Author "Pilz, Alexander"
Now showing items 1-12 of 12
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3-colorability of pseudo-triangulations
(2015)
Article
Open AccessDeciding 3-colorability for general plane graphs is known to be an NP-complete problem. However, for certain families of graphs, like triangulations, polynomial time algorithms exist. We consider the family of pseudo-tri ... -
A new lower bound on the maximum number of plane graphs using production matrices
(2018)
Conference lecture
Restricted access - publisher's policyWe use the concept of production matrices to show that there exist sets of n points in the plane that admit ¿(41.77n) crossing-free geometric graphs. This improves the previously best known bound of ¿(41.18n) by Aichholzer ... -
A new lower bound on the maximum number of plane graphs using production matrices
(2019-11-01)
Article
Open AccessWe use the concept of production matrices to show that there exist sets of n points in the plane that admit ¿(42.11n ) crossing-free geometric graphs. This improves the previously best known bound of ¿(41.18n ) by Aichholzer ... -
Cell-paths in mono- and bichromatic line arrangements in the plane
(2014)
Conference report
Open AccessWe show that in every arrangement of n red and blue lines | in general position and not all of the same color | there is a path through a linear number of cells where red and blue lines are crossed alternatingly (and no ... -
Characteristic polynomials of production matrices for geometric graphs
(2017-08-01)
Article
Open AccessAn n×n production matrix for a class of geometric graphs has the property that the numbers of these geometric graphs on up to n vertices can be read off from the powers of the matrix. Recently, we obtained such production ... -
Convex quadrangulations of bichromatic point sets
(2020-06-05)
Article
Open AccessWe consider quadrangulations of red and blue points in the plane where each face is convex and no edge connects two points of the same color. In particular, we show that the following problem is NP-hard: Given a finite set ... -
Empty triangles in good drawings of the complete graph
(2015)
Article
Open AccessA good drawing of a simple graph is a drawing on the sphere or, equivalently, in the plane in which vertices are drawn as distinct points, edges are drawn as Jordan arcs connecting their end vertices, and any pair of edges ... -
Geodesic order types
(2014-09-01)
Article
Restricted access - publisher's policyThe geodesic between two points a and b in the interior of a simple polygon P is the shortest polygonal path inside P that connects a to b. It is thus the natural generalization of straight line segments on unconstrained ... -
Lower bounds for the number of small convex k-holes
(2014-07-01)
Article
Open AccessLet S be a set of n points in the plane in general position, that is, no three points of S are on a line. We consider an Erdos-type question on the least number h(k)(n) of convex k-holes in S, and give improved lower bounds ... -
New results on stabbing segments with a polygon
(2015-01-01)
Article
Open AccessWe consider a natural variation of the concept of stabbing a set of segments with a simple polygon: a segment s is stabbed by a simple polygon P if at least one endpoint of s is contained in P, and a segment set S is stabbed ... -
New results on stabbing segments with a polygon
(Springer, 2013)
Conference report
Restricted access - publisher's policyWe consider a natural variation of the concept of stabbing a segment by a simple polygon: a segment is stabbed by a simple polygon P if at least one of its two endpoints is contained in P. A segment set S is stabbed by P ... -
Production matrices for geometric graphs
(2016)
Article
Open AccessWe present production matrices for non-crossing geometric graphs on point sets in convex position, which allow us to derive formulas for the numbers of such graphs. Several known identities for Catalan numbers, Ballot ...
