Physical Sciences and Mathematics Commons^™

Probabilistic And Extremal Problems In Combinatorics, Sean English

Dissertations

Graph theory as a mathematical branch has been studied rigorously for almost three centuries. In the past century, many new branches of graph theory have been proposed. One important branch of graph theory involves the study of extremal graph theory. In 1941, Turán studied one of the first extremal problems, namely trying to maximize the number of edges over all graphs which avoid having certain structures. Since then, a large body of work has been created in the study of similar problems. In this dissertation, a few different extremal problems are studied, but for hypergraphs rather than graphs. In particular, …