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- W1532861364 abstract "The 2- Disjoint Connected Subgraphs problem asks if a given graph has two vertex-disjoint connected subgraphs containing pre-specified sets of vertices. We show that this problem is NP-complete even if one of the sets has cardinality 2. The Longest Path Contractibility problem asks for the largest integer *** for which an input graph can be contracted to the path P *** on *** vertices. We show that the computational complexity of the Longest Path Contractibility problem restricted to P *** -free graphs jumps from being polynomially solvable to being NP-hard at ***= 6, while this jump occurs at ***= 5 for the 2- Disjoint Connected Subgraphs problem. We also present an exact algorithm that solves the 2- Disjoint Connected Subgraphs problem faster than ${cal O}^*(2^n)$ for any n -vertex P *** -free graph. For ***= 6, its running time is ${cal O}^*(1.5790^n)$. We modify this algorithm to solve the Longest Path Contractibility problem for P 6 -free graphs in ${cal O}^*(1.5790^n)$ time." @default.
- W1532861364 created "2016-06-24" @default.
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- W1532861364 date "2009-01-01" @default.
- W1532861364 modified "2023-10-17" @default.
- W1532861364 title "Partitioning Graphs into Connected Parts" @default.
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- W1532861364 doi "https://doi.org/10.1007/978-3-642-03351-3_15" @default.
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