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arXiv · 2407.19270

Computing the degreewidth of a digraph is hard

Pierre Aboulker·Nacim Oijid·Robin Petit·Mathis Rocton·Christopher-Lloyd Simon
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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 $1$, 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.

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Pierre Aboulker, Nacim Oijid, Robin Petit, Mathis Rocton, Christopher-Lloyd Simon. 2024-07-27. Computing the degreewidth of a digraph is hard. https://doi.org/10.46298/dmtcs.14299

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