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We present a linear time algorithm for computing linear layouts of trees which are optimal with respect to vertex separation. The best algorithm known so far is given by 7] and needs O(n log n) time. Our result solves several other related open problems on trees as for example the one of 17].

A graph is a tree of paths (cycles), if its vertex set can be partitioned into clusters, such that each cluster induces a simple path (cycle), and the clusters form a tree. Our main result states that the problem whether or not a given graph is a tree of paths (cycles) is NP-complete. Moreover, if the length of the paths (cycles) is bounded by a constant,… (More)

We introduce graph automata as devices for the recognition of linear graph languages. A graph automaton is the canonical extension of a nite state automaton recognizing a set of connected labeled graphs. It consists of a nite state control and a collection of heads, which search the input graph. In a move the graph automaton reads a new subgraph, checks… (More)

We consider the complexity of the emptiness problem for various classes of graph languages deened by eNCE (edge label neighborhood controlled embedding) graph grammars. In particular, we show that the emptiness problem is undecidable for general eNCE graph grammars, DEXPTIME-complete for connuent and boundary eNCE graph grammars, PSPACE-complete for linear… (More)

eNCE (edge label neighborhood controlled) graph grammars belong to the most powerful graph rewriting systems with single-node graphs on the left-hand side of the productions. From an algorithmic point of view, connuent and boundary eNCE graph grammars are the most interesting subclasses of eNCE graph grammars. In connuent eNCE graph grammars, the order in… (More)

We show that the following (equivalent) problems are P-complete: 1. Does a given connuent NCE graph grammar only generate graphs of bounded tree-width? and 2. is the graph language generated by a given connuent NCE graph grammar an HR language? This settles the complexity of these important problems on graph grammars .

The bounded K n;n-problem is the question whether or not a graph language of a given graph grammar contains arbitrarily large complete bipartite subgraphs K n;n. In this paper we investigate the complexity of this problem for all relevant classes of node replacement graph grammars.