Highly Non-Convex Crossing Sequences
Abstract
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.
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Cite this version of the work
Andrew McConvey
(2012).
Highly Non-Convex Crossing Sequences. UWSpace.
http://hdl.handle.net/10012/6749
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