Nacim Oijid Robin Petit’s scientific contributions

Given a digraph, an ordering of its vertices defines a \emph{backedge graph}, namely the undirected graph whose edges correspond to the arcs pointing backwards with respect to the order. The \emph{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.