Publication Date


Document Type


Committee Members

Anthony Evans (Committee Member), Daniel Slilaty (Advisor), Xiangqian Zhou (Committee Member)

Degree Name

Master of Science (MS)


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


Department or Program

Department of Mathematics and Statistics

Year Degree Awarded