Context-Free Graph Grammars: Separating Vertex Replacement from Hyperedge Replacement

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.

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