NLC-2 Graph Recognition and Isomorphism

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(n2m)-time algorithm, improving Johansson's algorithm [14]. Moreover, our alogrithm is simple to understand. The above properties and algorithm allow us to propose a robust O(n2m)-time isomorphism algorithm for NLC-2 graphs. As far as we know, it is the first polynomial-time algorithm.

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