Complexity of some arc-partition problems for digraphs

Jørgen Bang-Jensen (1) , Stéphane Bessy (2) , Daniel Gonçalves (2) , Lucas Picasarri-Arrieta (3)

1 SDU - University of Southern Denmark
2 LIRMM | ALGCO - Algorithmes, Graphes et Combinatoire
3 I3S - Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis

We study the complexity of deciding whether a given digraph D = (V, A) admits a partition (A1, A2) of its arc set such that each of the corresponding digraphs D1 = (V, A1) and D2 = (V, A2) satisfy some given prescribed property. We mainly focus on the following 15 properties: being bipartite, being connected, being strongly connected, being acyclic (spanning or not necessarily spanning), containing an in-branching, containing an out-branching, having some in-degree (or out-degree) conditions, satisfying some conditions on the number of arcs, being balanced (connected or not) or being a cycle. Combined with previous research, our work leads to a complete classification (in terms of being polynomial or NP-complete) of the complexity of 120 arc-partitioning problems on digraphs.

Mots clés: Digraphs; arc-partitions; NP-complete; polynomial algorithm; branchings; strong subdigraphs; cycle factor; acyclic digraph

Domaines: Informatique [cs]

Jørgen Bang-Jensen, Stéphane Bessy, Daniel Gonçalves, Lucas Picasarri-Arrieta. Complexity of some arc-partition problems for digraphs. Theoretical Computer Science, 2022, 928, pp.167-182. ⟨10.1016/j.tcs.2022.06.023⟩. ⟨hal-03699980⟩