More Fun with Symmetric Venn Diagrams

Abstract. Many researchers have had fun searching for and rendering symmetric Venn diagrams, culminating in the recent result of Griggs, Killian, and Savage ("Venn Diagrams and Symmetric Chain Decompositions in the Boolean Lattice," Electronic Journal of Combinatorics, 11 (2004), R2), that symmetric Venn diagrams on n curves exist if and only if n is prime. Our purpose here is to point out ways to prolong the fun by introducing and finding the basic properties of Venn and nearVenn diagrams that satisfy relaxed notions of symmetry, while leaving tantalizing open problems. A symmetric Venn diagram is one that possesses a rotational symmetry in the plane. A monochrome symmetric Venn diagram is one that is rotationally symmetric when the colours of the curves are ignored. A necessary condition for the existence of a monochrome symmetric Venn diagram is that the number of curves be a prime power. We specify conditions under which all curves must be non-congruent and give examples ...

• Type: Journal
• Year: 2006
• Where: MST
• Authors: Frank Ruskey, Mark Weston
• Keywords: Monochrome Symmetric Venn, MST 2006, Symmetric Venn Diagram, Venn Diagram