We establish that a set of graphs generated by a “Vertex replacement” graph grammar can be generated by a “Hyperedge replacement” one iff its graphs do not contain arbitrarily large complete bipartite graphs Kn,n as subgraphs, iff its graphs have a number of edges that is linearly bounded in terms of the number of vertices. These properties are decidable by means of an appropriate extension of the theorem by Parikh that characterizes the commutative images of context-free languages.
CITATION STYLE
Courcelle, B. (1993). Context-free graph grammars: Separating vertex replacement from hyperedge replacement. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 710 LNCS, pp. 181–193). Springer Verlag. https://doi.org/10.1007/3-540-57163-9_14
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