Embeddings of k-Connected Graphs of Pathwidth k
We present O( n 3) embedding algorithms (generalizing subgraph isomorphism) for classes of graphs of bounded pathwidth, where n is the number of vertices in the graph. These include the first polynomialtime algorithm for minor containment and the first O( n c) algorithm (c a constant independent of k) for topological embedding of graphs from subclasses of partial k-trees. Of independent interest are structural properties of k-connected graphs of bounded pathwidth on which our algorithms are based. We also describe special cases which reduce to various generalizations of string matching, permitting more efficient solutions.
KeywordsTree Decomposition Connected Subgraph Subgraph Isomorphism Path Decomposition Embedding Problem
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