This thesis considers circular flow-type and circular chromatic-type parameters (φ and χ, respectively) for matroids. In particular we focus on orientable matroids and 6 √ 1-matroids. These parameters are obtained via two approaches: algebraic and orientation-based. The general questions we discuss are: bounds for flow number; characterizations of Eulerian and bipartite matroids; and possible c...

A cycle of a matroid is a disjoint union of circuits. A cycle C of a matroidM is spanning if the rank of C equals the rank ofM . Settling an open problem of Bauer in 1985, Catlin in [P.A. Catlin, A reduction method to find spanning Eulerian subgraphs, J. Graph Theory 12 (1988) 29–44] showed that if G is a 2-connected graph on n > 16 vertices, and if δ(G) > n 5−1, thenGhas a spanning cycle. Catl...