Venn diagrams with few intersections

Simple item page
dc.contributor.authorBultena, Alberthaen_US
dc.date.accessioned2024-08-13T00:06:39Z
dc.date.available2024-08-13T00:06:39Z
dc.date.copyright1998en_US
dc.date.issued1998
dc.degree.departmentDepartment of Computer Science
dc.degree.levelMaster of Science M.Sc.en
dc.description.abstractThe n-Venn diagram is a collection of simple closed curves in the plane, intersecting only at point. The curves divide the plane into 2n open connected regions. Further, each region must contain a unique set of interiors of the curve. A region's weight is the number of curves that contain it. A monotone Venn diagram with n curves has the property that every region with weight k, where 1 <k <n, is adjacent to at least one region with weight k - 1 and at least one region with weight k + 1. An n-Venn diagram can be interpreted as a planar graph in which the intersection points of the curves are the vertices. We show that each monotone Venn diagram has at least ____ vertices and that this bound can be attained for all n > 1. For general Venn diagrams, the number of vertices is at least ______. Examples are given that demonstrate that this bound can be attained for 1 < n < 7.
dc.format.extent48 pages
dc.identifier.urihttps://hdl.handle.net/1828/17124
dc.rightsAvailable to the World Wide Weben_US
dc.titleVenn diagrams with few intersectionsen_US
dc.typeThesisen_US

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
BULTENA_Albertha_MSc_1998_941841.pdf
Size:
11.55 MB
Format:
Adobe Portable Document Format
Download

Collections

Electronic Theses and Dissertations (ETD)
 
University of Victoria Libraries

We acknowledge and respect the Lək̓ʷəŋən (Songhees and Esquimalt) Peoples on whose territory the university stands, and the Lək̓ʷəŋən and W̱SÁNEĆ Peoples whose historical relationships with the land continue to this day.