# 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