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- W2547414465 abstract "During the last decade, metric properties of the bags of tree-decompositions of graphs have been studied. Roughly, the length and the breadth of a tree-decomposition are the maximum diameter and radius of its bags respectively. The treelength and the treebreadth of a graph are the minimum length and breadth of its tree-decompositions respectively. Pathlength and pathbreadth are defined similarly for path-decompositions. In this paper, we answer open questions of [Dragan and Köhler, Algorithmica 2014] and [Dragan, Köhler and Leitert, SWAT 2014] about the computational complexity of treebreadth, pathbreadth and pathlength. Namely, we prove that computing these graph invariants is NP-hard. We further investigate graphs with treebreadth one, i.e., graphs that admit a tree-decomposition where each bag has a dominating vertex. We show that it is NP-complete to decide whether a graph belongs to this class. We then prove some structural properties of such graphs which allows us to design polynomial-time algorithms to decide whether a bipartite graph, resp., a planar graph, has treebreadth one." @default.
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- W2547414465 date "2016-01-01" @default.
- W2547414465 modified "2023-10-10" @default.
- W2547414465 title "On the Complexity of Computing Treebreadth" @default.
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- W2547414465 doi "https://doi.org/10.1007/978-3-319-44543-4_1" @default.
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