Publication Date
2017
Document Type
Thesis
Committee Members
Anthony Evans (Committee Member), Daniel Slilaty (Advisor), Xiangqian Zhou (Committee Member)
Degree Name
Master of Science (MS)
Abstract
Strong connectivity, 2-factors, and their relevance to Hamiltonicity, have been intensively studied on various classes of directed and 2-colored graphs. In chapter one, we define strong connectivity and bidirected 2-factors on bidirected graphs as a common genralization for both directed graphs and 2-colored graphs. We give necessary and sufficient conditions for the existence of bidirected Hamilton cycles in the following bidirected signed graphs: ± Kn, ± K{n,n}, and - K{n,n}. The Ramsey number problem is considered an interesting problem in graph theory which asks for the minimum positive integer r that assures a 2-colored complete Kr has a monochramatic clique Kn or Km. In chapter two, we define r*(n,m) to be the minimum positive integer that guarantees that any signing on Kr has, up to switching, - Kn or + Km. Also, the following results are obtained: r*(n,m) = r*(m,n), r*(n,m)≤ r(n-1,m-1)+1, r*(4,4)=7, r*(4,5) = 8, and 10 ≤ r*(4,6) ≤ 15.
Page Count
42
Department or Program
Department of Mathematics and Statistics
Year Degree Awarded
2017
Copyright
Copyright 2017, all rights reserved. My ETD will be available under the "Fair Use" terms of copyright law.
