✦ LIBER ✦

Planar acyclic oriented graphs

✍ Scribed by Carsten Thomassen

Book ID: 104736454
Publisher: Springer Netherlands
Year: 1989
Tongue: English
Weight: 725 KB
Volume: 5
Category: Article
ISSN: 0167-8094
DOI: 10.1007/bf00353654

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✦ Synopsis

A plane Hasse representation of an acyclic oriented graph is a drawing of the graph in the Euchdean 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.

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