×

Topological hypergraphs. (English) Zbl 1272.05137

Pach, János (ed.), Thirty essays on geometric graph theory. Berlin: Springer (ISBN 978-1-4614-0109-4/hbk; 978-1-4614-0110-0/ebook). 71-81 (2013).
Summary: Let \(P\) be a set of \(n\) points in the plane. A topological hypergraph \(G\), on the set of points of \(P\), is a collection of simple closed curves in the plane that avoid the points of \(P\). Each of these curves is called an edge of \(G\), and the points of \(P\) are called the vertices of \(G\). We provide bounds on the number of edges of topological hypergraphs in terms of the number of their vertices under various restrictions assuming the set of edges is a family of pseudo-circles.
For the entire collection see [Zbl 1256.05002].

MSC:

05C65 Hypergraphs
05C10 Planar graphs; geometric and topological aspects of graph theory
PDFBibTeX XMLCite
Full Text: DOI