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Drawings
Universal point sets for planar graphs ★★★
Author(s): Mohar
We say that a set is
-universal if every
vertex planar graph can be drawn in the plane so that each vertex maps to a distinct point in
, and all edges are (non-intersecting) straight line segments.
Question Does there exist an
-universal set of size
?
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
![$ O(n) $](/files/tex/ee18510ab4140627d7a8df7949d309533b39ebca.png)
Keywords: geometric graph; planar graph; universal set
Linear Hypergraphs with Dimension 3 ★★
Author(s): de Fraysseix; Ossona de Mendez; Rosenstiehl
Conjecture Any linear hypergraph with incidence poset of dimension at most 3 is the intersection hypergraph of a family of triangles and segments in the plane.
Keywords: Hypergraphs
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