NLC-2 graph recognition and isomorphism

Vincent Limouzy (1) , Fabien de Montgolfier (1) , Michael 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. 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.

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

Vincent Limouzy, Fabien de Montgolfier, Michael Rao. NLC-2 graph recognition and isomorphism. WG'07, 33rd International Workshop on Graph-Theoretic Concepts in Computer Science, 2007, Jena, Germany. ⟨hal-00159700⟩