Directed branch-width: A directed analogue of tree-width
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arXiv
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| Natura: | Preprint |
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2020
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| _version_ | 1866917931219156992 |
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| author | Bumpus, Benjamin Merlin Meeks, Kitty Pettersson, William |
| author_facet | Bumpus, Benjamin Merlin Meeks, Kitty Pettersson, William |
| contents | Gurski and Wanke showed that a graph class C has bounded tree-width if and only if its associated class of directed line graphs has bounded clique-width. Inevitably -- asking whether this relationship lifts to directed graphs -- we introduce a new digraph width measure: we obtain it by investigating digraphs whose directed line graphs have bounded cliquewidth. Thus, to generalize Gurski and Wanke's aforementioned result, we introduce a natural generalization of branch-width to digraphs and we name it accordingly.
Directed branch-width is a genuinely directed width-measure insofar as it cannot be used to bound the value of the underlying undirected tree-width. Despite this, the two measures are still closely related: the directed branch-width of a digraph D can differ from the branch-width of its underlying undirected graph only at sources and sinks. This relationship allows us to extend a range of algorithmic results from directed graphs with bounded underlying treewidth to the strictly larger class of digraphs having bounded directed branch-width. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_08903 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Directed branch-width: A directed analogue of tree-width Bumpus, Benjamin Merlin Meeks, Kitty Pettersson, William Combinatorics Computational Complexity Discrete Mathematics 05C75(Primary) 05C20, 05C76 (Secondary) G.2.2 Gurski and Wanke showed that a graph class C has bounded tree-width if and only if its associated class of directed line graphs has bounded clique-width. Inevitably -- asking whether this relationship lifts to directed graphs -- we introduce a new digraph width measure: we obtain it by investigating digraphs whose directed line graphs have bounded cliquewidth. Thus, to generalize Gurski and Wanke's aforementioned result, we introduce a natural generalization of branch-width to digraphs and we name it accordingly. Directed branch-width is a genuinely directed width-measure insofar as it cannot be used to bound the value of the underlying undirected tree-width. Despite this, the two measures are still closely related: the directed branch-width of a digraph D can differ from the branch-width of its underlying undirected graph only at sources and sinks. This relationship allows us to extend a range of algorithmic results from directed graphs with bounded underlying treewidth to the strictly larger class of digraphs having bounded directed branch-width. |
| title | Directed branch-width: A directed analogue of tree-width |
| topic | Combinatorics Computational Complexity Discrete Mathematics 05C75(Primary) 05C20, 05C76 (Secondary) G.2.2 |
| url | https://arxiv.org/abs/2009.08903 |