Computing the degreewidth of a digraph is hard
Combinatorics
2026-04-15 v5
Abstract
Given a digraph, an ordering of its vertices defines a backedge graph, namely the undirected graph whose edges correspond to the arcs pointing backwards with respect to the order. The degreewidth of a digraph is the minimum over all ordering of the maximum degree of the backedge graph. We answer an open question by Keeney and Lokshtanov [WG 2024], proving that it is \NP-hard to determine whether an oriented graph has degreewidth at most , which settles the last open case for oriented graphs. We complement this result with a general discussion on parameters defined using backedge graphs and their relations to classical parameters.
Cite
@article{arxiv.2407.19270,
title = {Computing the degreewidth of a digraph is hard},
author = {Pierre Aboulker and Nacim Oijid and Robin Petit and Mathis Rocton and Christopher-Lloyd Simon},
journal= {arXiv preprint arXiv:2407.19270},
year = {2026}
}