Thesiss

When dealing with hard problems, problems which we are not able to solve in polynomial time, it is common practice to preprocess an instance to reduce its size and make the task of solving it easier. Parameterized Complexity offers a theoretical framework to prove the efficiency…

Let G be a group, with X a G-conjugacy class of involutions. The local fusion graph F(G,X) has X as its vertex set, with vertices x, y in X joined by an edge if, and only if, x is not equal to y and the order of the product xy is odd. In this thesis we study these, and other rel…

A proper vertex coloring of a graph is an assignment of colors to all vertices such that adjacent vertices have distinct colors. The chromatic number χ(G) of a graph G is the minimum number of colors required for a proper vertex coloring. In this dissertation, we give some backg…

Since the dawn of the Information Age, we have increasingly relied on the technology that we develop to support nearly every aspect of modern living. At this point in our history, we are dependent on complex computer systems to manage and maintain the way our society and our wor…