A graph-theoretical axiomatization of oriented matroids
Kolja Knauer, Juan Jose Montellano-Ballesteros, Ricardo Strausz
TL;DR
This paper provides a graph-theoretical characterization of the systems of sign vectors that correspond to cocircuits of oriented matroids, offering a new axiomatic approach.
Contribution
It introduces a novel axiomatization of oriented matroids using the cocircuit graph, bridging combinatorial and graph-theoretical perspectives.
Findings
Characterizes cocircuits via the cocircuit graph
Provides axioms for oriented matroids based on graph properties
Enhances understanding of the structure of oriented matroids
Abstract
We characterize which systems of sign vectors are the cocircuits of an oriented matroid in terms of the cocircuit graph.
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Taxonomy
TopicsAdvanced Graph Theory Research · Advanced Algebra and Logic · Homotopy and Cohomology in Algebraic Topology