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A Sufficient Condition for Hamiltonian Connectedness in Standard 2-Colored Multigraphs

Abstract Details

2015, Master of Science, Miami University, Mathematics.
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.
Louis DiBiasio (Advisor)
Daniel Pritkin (Committee Member)
Tao Jiang (Committee Member)
15 p.

Recommended Citations

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)