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Graph theoretic closure properties of the family of boundary NLC graph languages

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Summary

Node label controlled (NLC) grammars are graph grammars (operating on node labeled undirected graphs) which rewrite single nodes only and establish connections between the embedded graph and the neighbors of the rewritten node on the basis of the labels of the involved nodes only. They define (possibly infinite) languages of undirected node labeled graphs (or, if we just omit the labels, languages of unlabeled graphs). Boundary NLC (BNLC) grammars are NLC grammars with the property that whenever — in a graph already generated — two nodes may be rewritten, then these nodes are not adjacent. The graph languages generated by this type of grammars are called BNLC languages.

The present paper continues the investigations of basic properties of BNLC grammars and languages where the central question is the following: “If L is a BNLC language and P is a graph theoretic property, is the set of all graphs from L satisfying P again a BNLC language?” We demonstrate that the class of BNLC languages is very “stable” in the sense that for almost all properties we consider the resulting languages are BNLC. In particular, the above question gets an affirmative answer, if the property P is: being k-colorable, being connected, having a subgraph homeomorphic to a given graph, and being nonplanar.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Computer Science, University of Leiden, Wassenaarseweg 80, Leiden, The Netherlands

    Grzegorz Rozenberg

  2. Institutes for Information Processing (IIG), Technical University of Graz and Austrian Computer Society, Schießstattgasse 4a, A-8010, Graz, Austria

    Emo Welzl

Authors
  1. Grzegorz Rozenberg
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  2. Emo Welzl
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Additional information

This research was carried out during the second author's stay at the Rijksuniversiteit Leiden, The Netherlands

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Rozenberg, G., Welzl, E. Graph theoretic closure properties of the family of boundary NLC graph languages. Acta Informatica 23, 289–309 (1986). https://doi.org/10.1007/BF00289115

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  • DOI: https://doi.org/10.1007/BF00289115

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