Which n-Venn diagrams can be drawn with convex k-gons?
| dc.creator | Carroll, Jeremy | |
| dc.creator | Ruskey, Frank | |
| dc.creator | Weston, Mark | |
| dc.date | 2005-11-30 | |
| dc.date.accessioned | 2026-07-07T06:53:46Z | |
| dc.date.available | 2026-07-07T06:53:46Z | |
| dc.description | We establish a new lower bound for the number of sides required for the component curves of simple Venn diagrams made from polygons. Specifically, for any n-Venn diagram of convex k-gons, we prove that k >= (2^n - 2 - n) / (n (n-2)). In the process we prove that Venn diagrams of seven curves, simple or not, cannot be formed from triangles. We then give an example achieving the new lower bound of a (simple, symmetric) Venn diagram of seven quadrilaterals. Previously Grunbaum had constructed a 7-Venn diagram of non-convex 5-gons [``Venn Diagrams II'', Geombinatorics 2:25-31, 1992]. | |
| dc.description | 10 pages, 3 figures. To be published in Proceedings of the Second International Workshop on Euler Diagrams (Euler 2005), Electronic Notes in Theoretical Computer Science | |
| dc.identifier | https://arxiv.org/abs/cs/0512001 | |
| dc.identifier | http://arxiv.org/abs/cs/0512001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/105704 | |
| dc.subject | Computational Geometry | |
| dc.subject | I.3.5 | |
| dc.title | Which n-Venn diagrams can be drawn with convex k-gons? | |
| dc.type | text |