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- W2029105149 abstract "A k-spanner of a graph G is a spanning subgraph of G in which the distance between any pair of vertices is at most k times the distance in G. We prove that for fixed k,w, the problem of deciding if a given graph has a k-spanner of treewidth w is fixed-parameter tractable on graphs of bounded degree. In particular, this implies that finding a k-spanner that is a tree (a tree k-spanner) is fixed-parameter tractable on graphs of bounded degree. In contrast, we observe that if the graph has only one vertex of unbounded degree, then Treek-Spanner is NP-complete for k?4. Research highlights? We study how to find a k-spanner of treewidth w in bounded degree graphs. ? We show that this problem is fixed-parameter tractable for fixed k,w. ? Hence Treek-Spanner is fpt on bounded degree graphs for fixed k. ? On graphs with a vertex of unbounded degree, the problem is NP-hard for k?4." @default.
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- W2029105149 date "2011-01-01" @default.
- W2029105149 modified "2023-09-25" @default.
- W2029105149 title "Spanners of bounded degree graphs" @default.
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- W2029105149 doi "https://doi.org/10.1016/j.ipl.2010.10.021" @default.
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