NLC-2 graph recognition and isomorphism

Vincent Limouzy (1) , Fabien de Montgolfier (1) , Michaël Rao (1)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

NLC-width is a variant of clique-width with many application in graph algorithmic. This paper is devoted to graphs of NLC-width two. After giving new structural properties of the class, we propose a $O(n^2 m)$-time algorithm, improving Johansson's algorithm~\cite{Johansson00}. Moreover, our alogrithm is simple to understand. The above properties and algorithm allow us to propose a robust $O(n^2 m)$-time isomorphism algorithm for NLC-2 graphs. As far as we know, it is the first polynomial-time algorithm.

Mots clés: NLC-width; Recognition; Algorithm; NLC-2 graphs; Isomorphism

Domaines: Algorithme et structure de données [cs.DS]

Vincent Limouzy, Fabien de Montgolfier, Michaël Rao. NLC-2 graph recognition and isomorphism. Graph-Theoretic Concepts in Computer Science 33rd International Workshop, WG 2007, Dornburg, Germany, June 21-23, 2007., Jun 2007, Dornburg, Germany. pp.86-98, ⟨10.1007/978-3-540-74839-7_9⟩. ⟨hal-00134605⟩