Half-Simple Symmetric Venn Diagrams
Chip Killian,
Department of Computer Science,
Duke University, USA.
Frank Ruskey,
Department of Computer Science,
University of Victoria, Canada.
Carla Savage,
Department of Computer Science,
North Carolina State University, USA.
Mark Weston,
Department of Computer Science,
University of Victoria, Canada.
Abstract:
A Venn diagram is simple if at most two curves intersect at any
given point.
A recent paper of Griggs, Killian, and Savage
[Elec. J. Combinatorics,
11 (2004) #R2]
shows how to construct rotationally symmetric Venn diagrams
for any prime number of curves.
However, the resulting diagrams contain only C(n,n/2)
intersection points, whereas a simple Venn diagram contains
2n-2 intersection points.
We show how to modify their construction to give symmetric
Venn diagrams with asymptotically at least
2n-1 intersection points,
whence the name "half-simple".
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Appears as:
C. Killian, F. Ruskey, C. Savage, and M. Weston,
Half-Simple Symmetric Venn Diagrams,
Electronic Journal of
Combinatorics,
11 (2004) #R86, 22 pages.
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The postscript file (colour figures).
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The pdf file (colour figures).
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Chip Killian is now a Ph.D. student at U.C. San Diego.
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xfig files for download (GKS = Griggs,Killian,Savage):
GKS 17,
GKS 19.
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