The complexity of deciding whether a graph admits an orientation with fixed weak diameter

Julien Bensmail (1) , Romaric Duvignau (1) , Sergey Kirgizov (2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 LIP6 - Laboratoire d'Informatique de Paris 6

An orientation of an undirected graph G has weak diameter k if, for every pair {u,v} of vertices of G, there is a directed path with length at most k joining u and v in either direction. In this work, we show that deciding whether a graph admits an orientation with weak diameter k is NP-complete whenever k>=2.

Domaines: Mathématique discrète [cs.DM]

Julien Bensmail, Romaric Duvignau, Sergey Kirgizov. The complexity of deciding whether a graph admits an orientation with fixed weak diameter. 2013. ⟨hal-00824250v1⟩