Some Results on Crossing Numbers
type: CreativeWork
description: 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.
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.
author: Lyczak, Alexander John
date published: 1971
date modified: 2026-07-24T03:47:40Z
provider: University of Pennsylvania
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Pennsylvania