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

TL;DR

This paper proves that determining whether a specific type of graph called an embedded caterpillar can be represented as weak unit disk contact graphs is an NP-hard problem, highlighting computational complexity challenges.

Contribution

It introduces a gadget-based reduction to establish the NP-hardness of recognizing embedded caterpillars with weak unit disk contact representations.

Findings

Recognition problem is NP-hard for embedded caterpillars.

Gadget-based reduction technique used for proof.

Highlights computational difficulty in geometric graph representations.

Abstract

Weak unit disk contact graphs are graphs that admit a representation of the nodes as a collection of internally disjoint unit disks whose boundaries touch if there is an edge between the corresponding nodes. We provide a gadget-based reduction to show that recognizing embedded caterpillars that admit a weak unit disk contact representation is NP-hard.