Half-simple symmetric Venn diagrams
The electronic journal of combinatorics, Tome 11 (2004) no. 1
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, Research Paper 2, 2004] 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."
@article{10_37236_1839,
author = {Charles E. Killian and Frank Ruskey and Carla D. Savage and Mark Weston},
title = {Half-simple symmetric {Venn} diagrams},
journal = {The electronic journal of combinatorics},
year = {2004},
volume = {11},
number = {1},
doi = {10.37236/1839},
zbl = {1060.05002},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1839/}
}
Charles E. Killian; Frank Ruskey; Carla D. Savage; Mark Weston. Half-simple symmetric Venn diagrams. The electronic journal of combinatorics, Tome 11 (2004) no. 1. doi: 10.37236/1839
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