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https://www.sciencedirect.com/science/article/pii/S0925772112000739
Biconvex point-sets are the only known point-sets of size n that universally support some class of planar graphs other than the outerplanar graphs. The relevance of the lattice constraint in our technique is evident in the base case of Lemma 10.Cited by: 20
https://www.researchgate.net/publication/221557306_On_Point-Sets_That_Support_Planar_Graphs
A universal point-set supports a crossing-free drawing of any planar graph. For a planar graph with n vertices, if bends on edges of the drawing are permitted, universal point-sets of size n are ...
https://hal.inria.fr/hal-00643824/document/
in general position [7]. Indeed, if the point-set is in convex position, then it supports exactly the family of outerplanar graphs. Determining other families of planar graphs for which universal point-sets of size n exist is an interesting problem. We examine a particular type of point-set, of sizeCited by: 20
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.361.6307
CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): A universal point-set supports a crossing-free drawing of any planar graph. For a planar graph with n vertices, if bends on edges of the drawing are permitted, universal point-sets of size n are known, but only if the bend points are in arbitrary positions. If the locations of the bend points must also be specified as ...
https://link.springer.com/chapter/10.1007/978-3-642-25878-7_7
Abstract. A universal point-set supports a crossing-free drawing of any planar graph. For a planar graph with n vertices, if bends on edges of the drawing are permitted, universal point-sets of size n are known, but only if the bend-points are in arbitrary positions. If the locations of the bend-points must also be specified as part of the point-set, we prove that any planar graph with n ...Cited by: 20
https://en.wikipedia.org/wiki/Universal_point_set
Special classes of graphs. Subclasses of the planar graphs may, in general, have smaller universal sets (sets of points that allow straight-line drawings of all n-vertex graphs in the subclass) than the full class of planar graphs, and in many cases universal point sets of exactly n points are possible.
https://www.cs.ubc.ca/~will/papers/universal.pdf
planar graphs for which it is universal. An application of this result to simultaneous embeddings and other consequences are discussed. Table 1 summarizes our results in terms of which sets of planar graphs can be supported on point-sets of a given cardinality with a speci ed number of bends.
https://www.academia.edu/13353453/On_Point-Sets_That_Support_Planar_Graphs
On Point-Sets That Support Planar Graphs
http://core.ac.uk/display/23287816
Abstract. A universal point-set supports a crossing-free drawing of any planar graph. For a planar graph with n vertices, if bends on edges of the drawing are permitted, universal point-sets of size n are known, but only if the bend points are in arbitrary positions.
https://en.wikipedia.org/wiki/Planar_graphs
Kuratowski's and Wagner's theorems. The Polish mathematician Kazimierz Kuratowski provided a characterization of planar graphs in terms of forbidden graphs, now known as Kuratowski's theorem: . A finite graph is planar if and only if it does not contain a subgraph that is a subdivision of the complete graph K 5 or the complete bipartite graph K 3,3 (utility graph).
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