For a given graph, G, the crossing number crₐ(G) denotes the minimum number of edge crossings when a graph is drawn on an orientable surface of genus a. The sequence cr₀(G), cr₁(G), ... is said to be the crossing sequence of a G. An equivalent definition exists for non-orientable surfaces.
In 1983, Jozef Širáň proved that for every decreasing, convex sequence of non-negative integers, there is a graph G such that this sequence is the crossing sequence of G. This main result of this thesis proves the existence of a graph with non-convex crossing sequence of arbitrary length.
Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OWTU.10012/6749 |
Date | January 2012 |
Creators | McConvey, Andrew |
Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
Language | English |
Detected Language | English |
Type | Thesis or Dissertation |
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