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Nick_Thesis_07312015.pdf (264.42 KB)
ETD Abstract Container
Abstract Header
A Sufficient Condition for Hamiltonian Connectedness in Standard 2-Colored Multigraphs
Author Info
Bruno, Nicholas J
ORCID® Identifier
http://orcid.org/0000-0001-9075-2756
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=miami1438385443
Abstract Details
Year and Degree
2015, Master of Science, Miami University, Mathematics.
Abstract
There have been many generalizations of Dirac's Theorem to more complex structures within graphs. I will present a proof that any standard 2-colored multigraph with minimum semi degree at least (1/2+ε)n is Hamiltonian Connected through paths of any color pattern. I will also present how this proof can be generalized to a much stronger condition that will relate to many previous results in this area. The proof will involve the idea of structures called Sorters and Pipelines and will follow closely the ideas within a proof by Haggkvist and Thomassen for arbitrarily oriented cycles in oriented graphs.
Committee
Louis DiBiasio (Advisor)
Daniel Pritkin (Committee Member)
Tao Jiang (Committee Member)
Pages
15 p.
Subject Headings
Mathematics
Keywords
graph theory, Dirac, combinatorics, Hamiltonian, H-linked, K-linked, multigraph, directed graph, colored graph, minimum degree, Hamiltonian cycles, Hamiltonian connected, Hamilton connected
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Refworks
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Citations
Bruno, N. J. (2015).
A Sufficient Condition for Hamiltonian Connectedness in Standard 2-Colored Multigraphs
[Master's thesis, Miami University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=miami1438385443
APA Style (7th edition)
Bruno, Nicholas.
A Sufficient Condition for Hamiltonian Connectedness in Standard 2-Colored Multigraphs.
2015. Miami University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=miami1438385443.
MLA Style (8th edition)
Bruno, Nicholas. "A Sufficient Condition for Hamiltonian Connectedness in Standard 2-Colored Multigraphs." Master's thesis, Miami University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=miami1438385443
Chicago Manual of Style (17th edition)
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Document number:
miami1438385443
Download Count:
412
Copyright Info
© 2015, some rights reserved.
A Sufficient Condition for Hamiltonian Connectedness in Standard 2-Colored Multigraphs by Nicholas J Bruno is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by Miami University and OhioLINK.