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arXiv · 2001.08982

Circuit-Difference Matroids

George Drummond·Tara Fife·Kevin Grace·James Oxley
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Abstract

One characterization of binary matroids is that the symmetric difference of every pair of intersecting circuits is a disjoint union of circuits. This paper considers circuit-difference matroids, that is, those matroids in which the symmetric difference of every pair of intersecting circuits is a single circuit. Our main result shows that a connected regular matroid is circuit-difference if and only if it contains no pair of skew circuits. Using a result of Pfeil, this enables us to explicitly determine all regular circuit-difference matroids. The class of circuit-difference matroids is not closed under minors, but it is closed under series minors. We characterize the infinitely many excluded series minors for the class.

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George Drummond, Tara Fife, Kevin Grace, James Oxley. 2020-01-24. Circuit-Difference Matroids. https://doi.org/10.37236/9314

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