# Extending Partial Representations of Unit Circular-arc Graphs

## TL;DR

This paper proves that extending partial representations of unit circular-arc graphs is an NP-complete problem, highlighting computational complexity challenges in graph representation extension tasks.

## Contribution

It establishes the NP-completeness of the partial representation extension problem specifically for unit circular-arc graphs, a previously unresolved question.

## Key findings

- Extension problem is NP-complete for unit circular-arc graphs
- Highlights computational difficulty in representation extension
- Advances understanding of graph recognition complexities

## Abstract

The partial representation extension problem, introduced by Klav\'{i}k et al. (2011), generalizes the recognition problem. In this short note we show that this problem is NP-complete for unit circular-arc graphs.