DeepAI AI Chat
Log In Sign Up

The Tree Stabbing Number is not Monotone

by   Wolfgang Mulzer, et al.

Let P ⊆ℝ^2 be a set of points and T be a spanning tree of P. The stabbing number of T is the maximum number of intersections any line in the plane determines with the edges of T. The tree stabbing number of P is the minimum stabbing number of any spanning tree of P. We prove that the tree stabbing number is not a monotone parameter, i.e., there exist point sets P ⊊ P' such that P > P', answering a question by Eppstein <cit.>.


page 1

page 2

page 3

page 4


Drawing a Rooted Tree as a Rooted y-Monotone Minimum Spanning Tree

Given a rooted point set P, the rooted y-Monotone Minimum Spanning Tree ...

Piercing Diametral Disks Induced by Edges of Maximum Spanning Tree

Let P be a set of points in the plane and let T be a maximum-weight span...

Grouping and Recognition of Dot Patterns with Straight Offset Polygons

When the boundary of a familiar object is shown by a series of isolated ...

Imposing edges in Minimum Spanning Tree

We are interested in the consequences of imposing edges in T a minimum s...

Uniform 2D-Monotone Minimum Spanning Graphs

A geometric graph G is xy-monotone if each pair of vertices of G is conn...

Drawing Tree-Based Phylogenetic Networks with Minimum Number of Crossings

In phylogenetics, tree-based networks are used to model and visualize th...

A Complete Set of Connectivity-aware Local Topology Manipulation Operations for Robot Swarms

The topology of a robotic swarm affects the convergence speed of consens...