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NLC-2 graph recognition and isomorphism

Vincent Limouzy·Fabien De Montgolfier·Michaël Rao
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Abstract

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.

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Vincent Limouzy, Fabien De Montgolfier, Michaël Rao. 2007-03-03. NLC-2 graph recognition and isomorphism. https://doi.org/10.1007/978-3-540-74839-7_9

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