Finding the circuits of a matroid

Minieka, Edward

doi:10.6028/jres.080b.034

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Symplectic Matroids Satisfying Circuit Axioms1

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Cited by 5 publications

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“…Throughout this section, B is the collection of bases of a symplectic matroid M, and C is the collection of minimal admissible subsets of E ±n not contained in any member of B. The expression of the unique circuit C and its proof for symplectic matroids is the same as those for ordinary matroids, which can be found in various papers or textbooks, for example, in [5].…”

Section: Symplectic Matroids Satisfying Circuit Axiomsmentioning

confidence: 99%

Symplectic Matroids, Circuits, and Signed Graphs

Tu¹

2018

Preprint

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One generalization of ordinary matroids is symplectic matroids. While symplectic matroids were initially defined by their collections of bases, there has been no cryptomorphic definition of symplectic matroids in terms of circuits. We give a definition of symplectic matroids by collections of circuits. As an application, we construct a class of examples of symplectic matroids from graphs in terms of circuits.

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Section: Symplectic Matroids Satisfying Circuit Axiomsmentioning

confidence: 99%