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• W2141667625 abstract "This thesis considers circular flow-type and circular chromatic-type parameters ($ and X, respectively) for matroids. In particular we focus on orientable matroids and fi-matroids. These parameters are obtained via two approaches: algebraic and orientation-based. The general questions we discuss are: bounds for flow number; characterizations of and bipartite matroids; and possible connections between the two possible extensions of $: algebraic and orientation. In the case of orientable matroids, we obtain characterizations of bipartite rank-3 matroids and uniform, rank-3 matroids; an asymptotic result regarding the flow number of uniform matroids; and an improvement on the known bound for flow number of matroids of arbitrary rank. This bound is further improved for the uniform case. For fi-matroids, we examine an algebraic extension of the parameters x and $. We also introduce a notion of orientation and the corresponding flow and chromatic numbers applicable to this class. We investigate the possibility of a connection between the algebraic and orientation-based parameters, akin to that established for regular matroids by Hoffman's Circulation Lemma and we obtain a partial connection. We extend the notion of Eulerian to fi-matroids. We call such matroids hex-Eulerian. We show that every maximum-sized $'i-matroid, of fixed rank, is hexEulerian. We also show that a regular matroid is hex-Eulerian if and only if it admits a nowhere-zero 3-flow. We include an extension of Tutte's chain groups, which characterize regular matroids, to what we term hex-chain modules which describe $'i-matroids." @default.
• W2141667625 created "2016-06-24" @default.
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• W2141667625 date "2007-01-01" @default.
• W2141667625 modified "2023-09-27" @default.
• W2141667625 title "Circular Flow and Circular Chromatic Number in the Matroid Context" @default.
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• W2141667625 hasPublicationYear "2007" @default.
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