# On the Clique-Width of Unigraphs

## TL;DR

This paper proves that all unigraphs have a clique-width of at most 4, implying many NP-hard problems become polynomial-time solvable on this class of graphs.

## Contribution

It establishes an upper bound of 4 on the clique-width of unigraphs, a class uniquely determined by their degree sequences.

## Key findings

- Unigraphs have clique-width at most 4.
- NP-hard problems are polynomial-time solvable on unigraphs.
- Provides a structural insight into unigraphs' complexity.

## Abstract

Clique-width is a well-studied graph parameter. For graphs of bounded clique-width, many problems that are NP-hard in general can be polynomial-time solvable. The fact motivates several studies to investigate whether the clique-width of graphs in a certain class is bounded or not. We focus on unigraphs, that is, graphs that are uniquely determined by their degree sequences up to isomorphism. We show that every unigraph has clique-width at most 4. It follows that many problems that are NP-hard in general are polynomial-time solvable for unigraphs.