Bipolar orientations revisited.

Hubert de Fraysseix (1) , Patrice Ossona de Mendez (1) , Pierre Rosenstiehl (1)

1 CAMS - Centre d'Analyse et de Mathématique sociales

Acyclic orientations with exactly one source and one sink - the so-called bipolar orientations - arise in many graph algorithms and specially in graph drawing. The fundamental properties of these orientations are explored in terms of circuits, cocircuits and also in terms of ``angles'' in the planar case. Classical results get here new simple proofs; new results concern the extension of partial orientations, exhaustive enumerations, the existence of deletable and contractable edges, and continuous transitions between bipolar orientations.

Mots clés: graph theory; bipolar orientation

Domaines: Combinatoire [math.CO]

Hubert de Fraysseix, Patrice Ossona de Mendez, Pierre Rosenstiehl. Bipolar orientations revisited.. Discrete Applied Mathematics, 1995, 56 (2-3), pp.157-179. ⟨10.1016/0166-218X(94)00085-R⟩. ⟨hal-00005622⟩