Representation of planar hypergraphs by contacts of triangles

3Citations
Citations of this article
9Readers
Mendeley users who have this article in their library.

This article is free to access.

Abstract

Many representation theorems extend from planar graphs to planar hypergraphs. The authors proved in [10] that every planar graph has a representation by contact of triangles. We prove here that this representation result extend to planar linear hypergraphs. Although the graph proof was simple and led to a linear time drawing algorithm, the extension for hypergraphs needs more work. The proof we give here relies on a combinatorial characterization of those hypergraphs which are representable by contact of segments in the plane, We propose some possible generalization directions and open problems, related to the order dimension of the incidence posets of hypergraphs. © 2008 Springer-Verlag Berlin Heidelberg.

Cite

CITATION STYLE

APA

De Fraysseix, H., Ossona De Mendez, P., & Rosenstiehl, P. (2008). Representation of planar hypergraphs by contacts of triangles. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4875 LNCS, pp. 125–136). https://doi.org/10.1007/978-3-540-77537-9_15

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free