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- W1544045550 abstract "We show that the complexity of the subgraph isomorphism problem on graphs of bounded path-width is inherently dependent on the connectivity of the source and target graphs. In particular, for the problem of determining whether a source graph G of path-width k is a subgraph of a target graph H of path-width k, we present an O(n3) algorithm for G and H both k-connected, for n the sum of the sizes of the graphs, and NP-completeness results for connectivity less than k. In previous polynomial-time algorithms, the degree of the polynomial in the running time was a function of k. In contrast, we show that when neither G nor H is k-connected, the problem becomes NP-complete. The same result also holds if one of the graphs has at least k vertices of unbounded degree. Since bounded path-width graphs are also bounded tree-width graphs, our hardness results immediately extend to this larger class. A further NP-completeness result applies to the situation in which both graphs have tree-width k, but only the target graph is k-connected. This provides a complete characterization of the subgraph isomorphism problem on bounded tree-width graphs, thus answering an open question of Matousek and Thomas." @default.
- W1544045550 created "2016-06-24" @default.
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- W1544045550 date "1996-01-01" @default.
- W1544045550 modified "2023-09-27" @default.
- W1544045550 title "Characterizing the complexity of subgraph isomorphism for graphs of bounded path-width" @default.
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- W1544045550 doi "https://doi.org/10.1007/3-540-60922-9_37" @default.
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