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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References
Chein, M., Habib, M., Maurer, M.C.: Partitive hypergraphs. Discrete Math. 37(1), 35–50 (1981)
Courcelle, B., Engelfriet, J., Rozenberg, G.: Handle-rewriting hypergraph grammars. J. Comput. Syst. Sci. 46(2), 218–270 (1993)
Cunningham, W.H.: Decomposition of directed graphs. SIAM J. Algebraic Discrete Methods 3(2), 214–228 (1982)
Cunningham, W.H., Edmonds, J.: A combinatorial decomposition theory. Canad. J. Math. 32, 734–765 (1980)
Dahlhaus, E.: Parallel algorithms for hierarchical clustering and applications to split decomposition and parity graph recognition. J. Algorithms 36(2), 205–240 (2000)
Dahlhaus, E., Gustedt, J., McConnell, R.M.: Partially complemented representations of digraphs. Discrete Math. Theor. Comput. Sci. 5(1), 147–168 (2002)
de Montgolfier, F., Rao, M.: The bi-join decomposition. In: ICGT. ENDM, vol. 22, pp. 173–177 (2005)
de Montgolfier, F., Rao, M.: Bipartitives families and the bi-join decomposition. Technical report (2005), https://hal.archives-ouvertes.fr/hal-00132862
Fouquet, J.-L., Giakoumakis, V., Vanherpe, J.-M.: Bipartite graphs totally decomposable by canonical decomposition. Internat. J. Found. Comput. Sci. 10(4), 513–533 (1999)
Gabor, C.P., Supowit, K.J., Hsu, W.-L.: Recognizing circle graphs in polynomial time. J. ACM 36(3), 435–473 (1989)
Gallai, T.: Transitiv orientierbare Graphen. Acta Math. Acad. Sci. Hungar. 18, 25–66 (1967)
Gurski, F., Wanke, E.: Minimizing NLC-width is NP-Complete. In: Kratsch, D. (ed.) WG 2005. LNCS, vol. 3787, pp. 69–80. Springer, Heidelberg (2005)
Habib, M., Paul, C., Viennot, L.: Partition refinement techniques: An interesting algorithmic tool kit. Internat. J. Found. Comput. Sci. 10(2), 147–170 (1999)
Johansson, Ö.: NLC\(_{\mbox{2}}\)-decomposition in polynomial time. Internat. J. Found. Comput. Sci. 11(3), 373–395 (2000)
McConnell, R.M., Spinrad, J.P.: Modular decomposition and transitive orientation. Discrete Math. 201(1-3), 189–241 (1999)
Wanke, E.: k-NLC Graphs and Polynomial Algorithms. Discrete Appl. Math. 54(2-3), 251–266 (1994)
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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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