Selected results in combinatorics and graph theory

Abstract

This dissertation is comprised of four different sets of combinatorial results which employ various graph-theoretic techniques. The first set of results is concerned with the number of independent sets in a graph; the second set of results develops a method for creating combinatorial designs from certain classes of graphs; the third set of results is concerned with the existence of alternating cycles in edge-colored graphs; and the fourth set of results guarantees the existence of Hamiltonian cycles in sparse pseudorandom bipartite graphs.