Directed branch-width: A directed analogue of tree-width [article]

Benjamin Merlin Bumpus, Kitty Meeks, William Pettersson
2023 arXiv   pre-print
We introduce a new digraph width measure called directed branch-width. To do this, we generalize a characterization of graph classes of bounded tree-width in terms of their line graphs to digraphs. Although we prove that underlying branch-width cannot be bounded in terms of our new measure, we show that directed branch-width is a natural generalization of its undirected counterpart and indeed the two invariants can be related via the operation of identifying pairs of sources or pairs of sinks.
more » ... everaging these operations and the relationship to underlying tree-width allows us to extend a range of algorithmic results from directed graphs with bounded underlying treewidth to the larger class of digraphs having bounded directed branch-width.
arXiv:2009.08903v2 fatcat:3buijtic7fc2jkexcw7jptbqnu