Abstract
The bounded Kn,n-problem is the question whether or not a graph language of a given graph grammar contains arbitrarily large complete bipartite subgraphs Kn,n. In this paper, we investigate the complexity of this problem for all relevant classes of node replacement graph grammers. Our main result states that the bounded Kn,n-problem is NL-complete for reduced nonblocking eNCE graph grammars and for reduced linear NCE graph grammars. As an application, our results settle the complexity of the problems whether or not the graph language of a given confluent, boundary, or linear graph grammar has bounded tree-width and whether or not it is an HR graph language.
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