The Linear Cutwidth and Cyclic Cutwidth of Complete n-Partite Graphs

<p>The cutwidth of different graphs is a topic that has been extensively studied. The basis of this paper is the cutwidth of complete <em>n</em>-partite graphs. While looking at the cutwidth of complete <em>n</em>-partite graphs, we strictly consider the linear embedding and cyclic embedding. The relationship between the linear cutwidth and the cyclic cutwidth is discussed and used throughout multiple proofs of different cases for the cyclic cutwidth. All the known cases for the linear and cyclic cutwidth of complete bipartite, complete tripartite, and complete <em>n</em>-partite graphs are highlighted.</p> <p>The main focus of this paper is to expand on the cyclic cutwidth of complete tripartite graphs. Using the relationship of the linear cutwidth and cyclic cutwidth of any graph, we find a lower bound and an upper bound for the cyclic cutwidth of complete tripartite graph K_(r,r,pr) where <em>r </em> is odd and <em>p</em> is a natural number. Throughout this proof there are two cases that develop, <em>p</em> even and <em>p</em> odd. Within each case we have to consider the cuts of multiple regions to find the maximum cut of the cyclic embedding. Once all regions within each case are considered, we discover that the upper and lower bounds are equivalent. This discovery of the cyclic cutwidth of complete tripartite graph K_(r,r,pr) where r is odd and <em>p</em> is a natural number results in getting one step closer to finding the cyclic cutwidth of any complete tripartite graph K_(r,s,t).</p>

Name thesis:degree_name

Master of Arts in Mathematics

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2014

Author dc:creator

• Creswell, Stephanie A

Contributors dc:contributor

• Dr. Joseph Chavez

• Cutwidth
• n-Partite
• Linear
• Cyclic
• Tripartite
• Bipartite
• Discrete Mathematics and Combinatorics
• Mathematics

Repository record dc:identifier

https://scholarworks.lib.csusb.edu/etd/34

OAI identifier oai:identifier

oai:scholarworks.lib.csusb.edu:etd-1081