THE ELECTRONIC JOURNAL OF COMBINATORICS (ed. June 2005), DS#5.

A Survey of Venn Diagrams

Department of Computer Science

University of Victoria

Victoria, B.C. V8W 3P6

CANADA

Note: This is an updated version of a survey that first appeared as a Dynamic Survey in February, 1997, and was revised in 2001 and 2005. There is a summary of changes.

The official version of this survey is at the Electronic Journal of Combinatorics. This version is the local working version of the authors. Use at your own risk.

The purpose of these pages is to collect together various facts and figures about Venn diagrams, particularly as they relate to combinatorial and geometric properties of the diagrams. Aperiodic updates are planned and comments and suggestions are most welcome.

- Who was John Venn?
- What is a Venn diagram?
- Formal definition of Venn diagrams

The Borromean Rings - General constructions of Venn diagrams

- Formal definition of Venn diagrams
- Graphs associated with Venn diagrams.
- The planar dual of a Venn diagram

Venn dual graphs of Venn's construction - When are two Venn diagrams different?

Separating vertices - How many Venn diagrams are there?
- Extending Venn diagrams

An irreducible diagram - Minimum vertex Venn diagrams

Minimum 5-Venn diagrams - Congruent Venn diagrams

- The planar dual of a Venn diagram
- Symmetric Venn diagrams.
- Rotational Symmetry

Symmetric diagrams for small*n* - A general construction for symmetric diagrams

Symmetric diagrams and necklaces

Variants on Symmetry- Symmetry for non-prime
*n* - Venn diagrams and Gray codes

Gray codes and Edwards' construction

- Symmetry for non-prime

- Rotational Symmetry
- Geometric Variations.
- Convexity

Six triangles - Exposure
- Area-proportional diagrams

Poly-Venn diagrams for 6 and 7 sets

- Convexity
- Generalizations and Extensions of Venn diagrams.
- Relaxations of parameters
*k*-fold 2-Venn diagrams - Generalizing symmetry
- Euler diagrams

- Relaxations of parameters
- Open problems.
- References.
- Acknowledgements.
- Footnotes.

The icon to the left appears on all the following pages.
Clicking on it will bring you back to this page.

The 7-fold rosette at the top of the page is a Venn diagram for
*n* = 7, called "Victoria." Find out more about it by going
to the page on symmetric Venn diagrams for small *n*.

There are some Venn diagrams on the pages to follow that have not
appeared before in the literature, in particular, most of the
symmetric Venn diagrams for *n*=7.

All the Venn diagram figures to be found on the following pages, unless otherwise noted, are © the authors and are not to be used without written permission from the authors.

Received: August 28, 1996.

Previous editions: February 2 1997, March 15 2001.

Current edition: June 10 2005.

THE ELECTRONIC JOURNAL OF COMBINATORICS (ed. June 2005), DS #5. |