Nowhere-zero flows and structure theory for signed graphs

This thesis explores two variations of signed graphs. For the first variation we study nowhere-zero flows. Here we develop algorithms for computing the circular flow number in cubic graphs and we establish some theorems giving bounds on the circular flow number. For the second variation we prove a theorem showing the existence of a decomposition of a signed graph into positive cycles and a related theorem implying the existence of a removable cycle. We also establish a new structure theorem characterizing when a 3-connected signed graph has a path between two distinguished vertices that is disjoint from a negative cycle.