Ossona de Mendez, Patrice
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
Straight line representation of planar linear hypergraphs ★★
Author(s): de Fraysseix; Ossona de Mendez
Conjecture Every planar linear hypergraph has a straight line representation in the plane which maps each vertex to a point and each edge to a straight line segment , in such a way that:
- \item for each vertex and each edge , we have: \item for each couple of distinct edges , we have
Keywords: intersection graph; planar hypergraph