On the Minimum Number of Inversions to Make a Digraph k‐(Arc‐)Strong
Year: 2025
Type: article
Abstract: ABSTRACT The inversion of a set of vertices in a digraph consists of reversing the direction of all arcs of . We study (resp., ) which is (for some positive integer ) the minimum number of inversions needed to transform into a ‐arc‐strong (resp., ‐strong) digraph or if no such transformation exists. Note that . We set . We show the following results where is a fixed integer for : for every ; for any fixed positive integer , deciding whether a given oriented graph with satisfies is NP‐complete; for any fixed positive integer , deciding whether a given oriented graph with satisfies is NP‐complete; if is a tournament of order at least , then , and ; for some tournament of order ; if is a tournament of order at least (resp., ), then (resp., ); for every , there exists such that for every positive integer and every tournament on at least vertices, we have .
Source: Journal of Graph Theory
DOI: 10.1002/jgt.23290
Institutions: University of Warsaw, Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Université Côte d'Azur, Laboratoire d'Informatique, Signaux et Systèmes de Sophia Antipolis, Helmholtz Center for Information Security, Université Paris Sciences et Lettres, École Normale Supérieure - PSL, Département d'Informatique
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417181526