Log In Sign Up

Weak Unit Disk Contact Representations for Graphs without Embedding

by   Jonas Cleve, et al.

Weak unit disk contact graphs are graphs that admit representing nodes as a collection of internally disjoint unit disks whose boundaries touch if there is an edge between the corresponding nodes. In this work we focus on graphs without embedding, i.e., the neighbor order can be chosen arbitrarily. We give a linear time algorithm to recognize whether a caterpillar, a graph where every node is adjacent to or on a central path, allows a weak unit disk contact representation. On the other hand, we show that it is NP-hard to decide whether a tree allows such a representation.


page 3

page 4

page 5

page 6

page 7


Recognizing embedded caterpillars with weak unit disk contact representations is NP-hard

Weak unit disk contact graphs are graphs that admit a representation of ...

Unit Disk Representations of Embedded Trees, Outerplanar and Multi-Legged Graphs

A unit disk intersection representation (UDR) of a graph G represents ea...

Layered Area-Proportional Rectangle Contact Representations

We investigate two optimization problems on area-proportional rectangle ...

Being Corrupt Requires Being Clever, But Detecting Corruption Doesn't

We consider a variation of the problem of corruption detection on networ...

On Arrangements of Orthogonal Circles

In this paper, we study arrangements of orthogonal circles, that is, arr...

Representing Graphs and Hypergraphs by Touching Polygons in 3D

Contact representations of graphs have a long history. Most research h...

Axes-parallel unit disk graph recognition is NP-hard

Unit disk graphs are the intersection graphs of unit diameter disks in t...