Polynomial-time Algorithm for Isomorphism of Graphs with Clique-width at most Three

TL;DR

This paper presents a polynomial-time algorithm specifically for testing isomorphism of graphs with clique-width at most three, expanding the class of graphs with efficiently solvable isomorphism problems.

Contribution

It introduces a polynomial-time algorithm for graph isomorphism in graphs with clique-width at most three, independent of prior work on bounded clique-width graphs.

Findings

Polynomial-time algorithm for clique-width ≤ 3 graphs

Independent of previous polynomial-time results for bounded clique-width

Advances understanding of graph isomorphism complexity

Abstract

The clique-width is a measure of complexity of decomposing graphs into certain tree-like structures. The class of graphs with bounded clique-width contains bounded tree-width graphs. We give a polynomial time graph isomorphism algorithm for graphs with clique-width at most three. Our work is independent of the work by Grohe et al. \cite{grohe2015isomorphism} showing that the isomorphism problem for graphs of bounded clique-width is polynomial time.