Generating All Simple Convexly-Drawable Polar Symmetric 6-Venn Diagrams
Khalegh Mamakani,
Department of Computer Science,
University of Victoria, Canada.
Wendy Myrvold,
Department of Computer Science,
University of Victoria, Canada.
Frank Ruskey,
Department of Computer Science,
University of Victoria, Canada.
Abstract:
An n-Venn diagram consists of n curves drawn in the plane in
such a way that each of the 2n possible intersections of the
interiors and exteriors of the curves forms a connected non-empty region.
A Venn diagram is convexly-drawable if it can be drawn with all curves convex and it
is simple if at most two curves intersect at any point.
A Venn diagram is called polar symmetric if its stereographic
projection about the infinite outer face is isomorphic to the
projection about the innermost face.
We outline an algorithm that shows there are exactly 375 simple convexly
drawable polar-symmetric
6-Venn diagrams.
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Here are a couple of polar symmetric monotone 6-Venn diagrams
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Files: pdf.
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A full list of all 375 diagrams:
PolarSixVenn.html.
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Submitted February 22, 2011 to IWOCA 2011.
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Accepted and presented at IWOCA 2011 by Khalegh.
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Appears in LNCS 7056 (2011) 275-286.
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