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You searched for subject:(irreducible triangulation). One record found.

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1. Campbell, Russell J. Finding obstructions within irreducible triangulations.

Degree: Department of Computer Science, 2017, University of Victoria

The 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. Advisors/Committee Members: Myrvold, Wendy (supervisor).

Subjects/Keywords: graph theory; topological graph theory; obstruction; embedding algorithm; irreducible triangulation; torus; projective plane; Klein bottle

triangulation of the surface. A triangulation is irreducible if it has no contractible edges, and it… …7.26 A1 obstruction of N1 — Kc4 triangulation of N2 . A2 obstruction of N1 — Kh6… …triangulation of N2 . B1 obstruction of N1 — Kh6 triangulation of N2 . B3 obstruction of N1 — Kh6… …triangulation of N2 . C7 obstruction of N1 — Kh4 triangulation of N2 . D9 obstruction of N1 — Kh25… …triangulation of N2 D12 obstruction of N1 — Kh7 triangulation of N2 . D17 obstruction of N1 — Kh1… 

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Campbell, R. J. (2017). Finding obstructions within irreducible triangulations. (Thesis). University of Victoria. Retrieved from http://hdl.handle.net/1828/8212

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Campbell, Russell J. “Finding obstructions within irreducible triangulations.” 2017. Thesis, University of Victoria. Accessed July 10, 2020. http://hdl.handle.net/1828/8212.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Campbell, Russell J. “Finding obstructions within irreducible triangulations.” 2017. Web. 10 Jul 2020.

Vancouver:

Campbell RJ. Finding obstructions within irreducible triangulations. [Internet] [Thesis]. University of Victoria; 2017. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/1828/8212.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Campbell RJ. Finding obstructions within irreducible triangulations. [Thesis]. University of Victoria; 2017. Available from: http://hdl.handle.net/1828/8212

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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