Finding obstructions within irreducible triangulations

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dc.contributor.authorCampbell, Russell J.
dc.contributor.supervisorMyrvold, Wendy
dc.date.accessioned2017-06-01T22:40:11Z
dc.date.available2017-06-01T22:40:11Z
dc.date.copyright2017en_US
dc.date.issued2017-06-01
dc.degree.departmentDepartment of Computer Scienceen_US
dc.degree.levelDoctor of Philosophy Ph.D.en_US
dc.description.abstractThe main results of this dissertation show evidence supporting the Successive Surface Scaffolding Conjecture. This is a new conjecture that, if true, guarantees the existence of all the wye-delta-order minimal obstructions of a surface S as subgraphs of the irreducible triangulations of the surface S with a crosscap added. A new data structure, i.e. an augmented rotation system, is presented and used to create an exponential-time algorithm for embedding graphs in any surface with a constant-time check of the change in genus when inserting an edge. A depiction is a new formal definition for representing an embedding graphically, and it is shown that more than one depiction can be given for nonplanar embeddings, and that sometimes two depictions for the same embedding can be drastically different from each other. An algorithm for finding the essential cycles of an embedding is given, and is used to confirm for the projective-plane obstructions, a theorem that shows any embedding of an obstruction must have every edge in an essential cycle. Obstructions of a general surface S that are minor-minimal and not double-wye-delta-minimal are shown to each have an embedding on the surface S with a crosscap added. Finally, open questions for further research are presented.en_US
dc.description.scholarlevelGraduateen_US
dc.identifier.urihttp://hdl.handle.net/1828/8212
dc.languageEnglisheng
dc.language.isoenen_US
dc.rightsAvailable to the World Wide Weben_US
dc.subjectgraph theoryen_US
dc.subjecttopological graph theoryen_US
dc.subjectobstructionen_US
dc.subjectembedding algorithmen_US
dc.subjectirreducible triangulationen_US
dc.subjecttorusen_US
dc.subjectprojective planeen_US
dc.subjectKlein bottleen_US
dc.titleFinding obstructions within irreducible triangulationsen_US
dc.typeThesisen_US

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