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On universal point sets for planar graphs

par Cardinal, Jean ;Hoffmann, Michael;Kusters, Vincent
Référence Lecture notes in computer science, 8296 LNCS, page (30-41)
Publication Publié, 2013

Article révisé par les pairs

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Résumé :

A set P of points in ℝ2 is n-universal, if every planar graph on n vertices admits a plane straight-line embedding on P. Answering a question by Kobourov, we show that there is no n-universal point set of size n, for any n ≥ 15. Conversely, we use a computer program to show that there exist universal point sets for all n ≤ 10 and to enumerate all corresponding order types. Finally, we describe a collection of G of 7'393 planar graphs on 35 vertices that do not admit a simultaneous geometric embedding without mapping, that is, no set of 35 points in the plane supports a plane straight-line embedding of all graphs in G. © 2013 Springer-Verlag.