Lecture Notes in Computer Science Volume 5417, 2009, pp 396-407

Subdivision Drawings of Hypergraphs

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Abstract

We introduce the concept of subdivision drawings of hypergraphs. In a subdivision drawing each vertex corresponds uniquely to a face of a planar subdivision and, for each hyperedge, the union of the faces corresponding to the vertices incident to that hyperedge is connected. Vertex-based Venn diagrams and concrete Euler diagrams are both subdivision drawings. In this paper we study two new types of subdivision drawings which are more general than concrete Euler diagrams and more restricted than vertex-based Venn diagrams. They allow us to draw more hypergraphs than the former while having better aesthetic properties than the latter.

This research was initiated during the Bertinoro Workshop on Graph Drawing, 2008. Bettina Speckmann is supported by the Netherlands Organisation for Scientific Research (NWO) under project no. 639.022.707.