Discrete Mathematics· 2026Q1
Directed branch-width: A directed analogue of tree-width
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- Q1SCImago
- 2026year
Short summary
Researchers introduce directed branch-width, a new measure for directed graphs that is distinct from undirected tree-width, enabling algorithmic extensions to a broader class of digraphs.
AI-generated from the title and abstract; the full text is not read.
Key points
- Introduces directed branch-width, a novel width measure for directed graphs.
- Directed branch-width is distinct from undirected tree-width and cannot bound it.
- The measure differs from undirected tree-width only at sources and sinks.
- Enables extension of algorithmic results to digraphs with bounded directed branch-width.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. Discrete Mathematics, 2026 · DOI ↗
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Field: Computational Theory and Mathematics
Computational Theory and MathematicsComputer Science