Order

, Volume 5, Issue 4, pp 349–361

Planar acyclic oriented graphs

  • Carsten Thomassen
Article

Abstract

A plane Hasse representation of an acyclic oriented graph is a drawing of the graph in the Euclidean plane such that all arcs are straight-line segments directed upwards and such that no two arcs cross. We characterize completely those oriented graphs which have a plane Hasse representation such that all faces are bounded by convex polygons. From this we derive the Hasse representation analogue, due to Kelly and Rival of Fary's theorem on straight-line representations of planar graphs and the Kuratowski type theorem of Platt for acyclic oriented graphs with only one source and one sink. Finally, we describe completely those acyclic oriented graphs which have a vertex dominating all other vertices and which have no plane Hasse representation, a problem posed by Trotter.

AMS subject classifications (1980)

05C10 06A10 

Key words

Convex Hasse representations Kuratowski type results for Hasse diagrams 

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Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Carsten Thomassen
    • 1
  1. 1.Mathematical InstituteThe Technical University of DenmarkLyngbyDenmark

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