An extension of matroid rank submodularity and the -Rayleigh property.

In this paper, we prove that an element splitting operation by every pair of elements on a cographic matroid yields a cographic matroid if and only if it has no minor isomorphic to M(K₄).

Broken Circuits in Matroids-Dohmen’s Inductive Proof

Wojciech Kordecki, Anna Łyczkowska-Hanćkowiak (2013)

Discussiones Mathematicae Graph Theory

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Dohmen [4] gives a simple inductive proof of Whitney’s famous broken circuits theorem. We generalise his inductive proof to the case of matroids

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Broken Circuits in Matroids-Dohmen’s Inductive Proof

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