Date of Award
1971
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Graduate Group
Mathematics
First Advisor
Herbert Wilf
Abstract
The drawing of the complete graph in which the vertices are placed on the rims of a cylinder and connected with geodesic edges is conjectured to produce the minimum number of edge crossings for a complete graph, which is its crossing number. This dissertation proves that no edge in this drawing can be redrawn to reduce the total number of edge crossings.
Recommended Citation
Lyczak, Alexander John Jr., "Some Results on Crossing Numbers" (1971). Publicly Accessible Penn Dissertations. 4286.
https://repository.upenn.edu/edissertations/4286
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