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• W2073919081 abstract "We present a clear demarcation between classes of bounded tree-width graphs for which the subgraph isomorphism problem is NP-complete and those for which it can be solved in polynomial time. In previous work, it has been shown that this problem is solvable in polynomial time if the source graph either has bounded degree or is k -connected, for k the tree-width of the two graphs. As well, it has also been shown that for certain specific connectivity or degree conditions, the problem becomes NP-complete. Here we give a complete characterization of the complexity of this problem on bounded tree-width graphs for all possible connectivity conditions of the two input graphs. Specifically, we show that when the source graph is not k -connected or has more than k vertices of unbounded degree the problem is NP-complete; this answers an open question of Matoušek and Thomas. Many of our reductions are restricted to using a subset of graphs of bounded tree-width, namely graphs of bounded path-width. As a direct result of our constructions, we also show that when the source and target graphs have connectivity less than k or at least one has k vertices of unbounded degree, the subgraph isomorphism problem for bounded path-width graphs is NP-complete." @default.
• W2073919081 created "2016-06-24" @default.
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• W2073919081 date "1996-09-01" @default.
• W2073919081 modified "2023-10-16" @default.
• W2073919081 title "The complexity of subgraph isomorphism for classes of partial k-trees" @default.
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• W2073919081 doi "https://doi.org/10.1016/0304-3975(96)00046-1" @default.
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