Half-simple symmetric Venn diagrams
type: Item
instance of: scholarly article
title: Half-simple symmetric Venn diagrams
zbMATH Open document ID: 1060.05002
author: Charles E. Killian
author: Frank Ruskey
author: Carla D. Savage
author: Mark Weston
published in: The Electronic Journal of Combinatorics
publication date: 2005-04-25T00:00:00Z
full work available at URL: https://eudml.org/doc/124409
full work available at URL: v11i1r86.html
review text: Summary: A Venn diagram is simple if at most two curves intersect at any given point. A recent paper of \textit{J. Griggs} et al. [Electron. J. Comb., Research paper R2 (2004; Zbl 1034.06001)] shows how to construct rotationally symmetric Venn diagrams for any prime number of curves. However, the resulting diagrams contain only \({n \choose {\lfloor n/2 \rfloor}}\) intersection points, whereas a simple Venn diagram contains \(2^n-2\) intersection points. We show how to modify their construction to give symmetric Venn diagrams with asymptotically at least \(2^{n-1}\) intersection points, whence the name ``half-simple.''
Mathematics Subject Classification ID: 05A10
Mathematics Subject Classification ID: 06A07
zbMATH DE Number: 2161277
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2161277