Abstract
Graph grammars are widely used in order to define classes of graphs having some inductive and narrow structure. It is known, that graph classes defined by context-free graph grammars have bounded clique-width, but this general observation does not give the bound on the clique-width explicitly.
We investigate here the explicit relationship between various not necessarily context-free Neighborhood Controlled Embedding (NCE) graph grammars and the clique-width of graphs generated by them. We show that all the graphs, generated by any given NCE graph grammar, have an explicitly computable bounded clique-width (where the bound depends only on parameters of the grammar), and provide the corresponding algorithms (based on dynamic programming techniques) for finding clique-width expression based on given derivation tree.
All the results are first obtained for Node Label Controlled (NLC) grammars, but can be generalized to both NCE grammars and edNCE grammars (for directed graphs with dynamic edge relabelling).
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Glikson, A., Makowsky, J.A. (2003). NCE Graph Grammars and Clique-Width. In: Bodlaender, H.L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2003. Lecture Notes in Computer Science, vol 2880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39890-5_21
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DOI: https://doi.org/10.1007/978-3-540-39890-5_21
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