Off-campus UNL users: To download campus access dissertations, please use the following link to log into our proxy server with your NU ID and password. When you are done browsing please remember to return to this page and log out.
Non-UNL users: Please talk to your librarian about requesting this dissertation through interlibrary loan.
Four Mathematical Results on a Theme by Paganini
In this thesis we explore four different problems, related through their use of graph theory. Firstly, we look at a pursuit game variant on graphs called Hunters and Rabbits and determine the parameters of this game for the hypercube, as well as a broader class of well behaved graphs. Secondly, we determine the maximum clique count across graphs of a fixed size under a maximum degree condition and a property of their clique complexes called shellability. Thirdly, we show that the 2-matching polynomial of a graph is always integral and identify a necessary and sufficient condition for a graph cover to be normal based only on its permutation representation. Lastly, we introduce two versions of the "deck transformation monoid" formed by taking the partial deck transformations of a space which respect a given immersion with and without a connected condition. We then explore the properties of these two variants and partial analogues to covering space theory.^
Groothuis, Corbin, "Four Mathematical Results on a Theme by Paganini" (2018). ETD collection for University of Nebraska - Lincoln. AAI10793320.