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Complexity of finding embeddings in a k-tree. (English) Zbl 0611.05022
A k-tree is an undirected graph that can be reduced to the k-complete graph by a sequence of removals of k-degree vertices with completely connected neighbors. A partial k-tree is a subgraph of a k-tree; $$k_ t(G)$$ is the smallest k for which G is a partial k-tree.
The problem PARTIAL K-TREE is: given a graph G and an integer k, is $$k_ t(G)\leq k?$$ The authors prove that PARTIAL K-TREE problem is NP-complete. For a fixed k, they present a polynomial time algorithm for that problem which, unfortunately, is of degree k.
Reviewer: G.Slutzki

##### MSC:
 05C10 Planar graphs; geometric and topological aspects of graph theory 68Q25 Analysis of algorithms and problem complexity 90C39 Dynamic programming
##### Keywords:
algorithm complexity; NP completeness; k-tree
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