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dc.contributor.authorMcConvey, Andrew 21:47:40 (GMT) 21:47:40 (GMT)
dc.description.abstractFor 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.en
dc.publisherUniversity of Waterlooen
dc.subjectGraph Theoryen
dc.subjectCrossing Numbersen
dc.subjectCrossing Sequencesen
dc.titleHighly Non-Convex Crossing Sequencesen
dc.typeMaster Thesisen
dc.subject.programCombinatorics and Optimizationen and Optimizationen
uws-etd.degreeMaster of Mathematicsen

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