On Universal Point Sets for Planar Graphs

Jean Cardinal, Michael Hoffmann, Vincent Kusters
2015 Journal of Graph Algorithms and Applications  
A set P of points in R 2 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 G of 7 393 planar graphs on 35 vertices that do not admit a simultaneous geometric
more » ... ing without mapping, that is, no set of 35 points in the plane supports a plane straight-line embedding of all graphs in G.
doi:10.7155/jgaa.00374 fatcat:ehvzq7d4ezb3dpzpik7a6rbk4y