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 [14]. 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.
Research supported by the ANR project Graph Decompositions and Algorithms (GRAAL) and by INRIA project-team Gang.
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Limouzy, V., de Montgolfier, F., Rao, M. (2007). NLC-2 Graph Recognition and Isomorphism. In: Brandstädt, A., Kratsch, D., Müller, H. (eds) Graph-Theoretic Concepts in Computer Science. WG 2007. Lecture Notes in Computer Science, vol 4769. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74839-7_9
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DOI: https://doi.org/10.1007/978-3-540-74839-7_9
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