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.
Jan 23, 2020
Jan 24, 2020 · 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 ...
People also ask
What is a circuit in a matroid?
What is the concept of Matroids?
What is the basis exchange property of Matroids?
circuit-difference matroids, that is, those matroids in which the symmetric difference. of every pair of intersecting circuits is a single circuit. Our main ...
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, thoseMatroids in which the symmetric difference of every pair of intersecting circuits is a ...
Apr 8, 2016 · One of the axioms of the circuits of a matroid is that any two are incomparable, that is, if C1⊆C2 are circuits of a matroid, then C1=C2.
May 3, 2022 · Every even circuit in a connected, non-affine, binary matroid is the symmetric difference of two odd circuits. In a connected matroid M with ...
Aug 3, 2021 · The dimension of the circuit space of a matroid M is the corank of M if and only if M is binary. Here is a proof. Given a basis B and e∉B, ...
A circuit basis for a matroid is a least set of circuits which will generate all the circuits of the matroid by repeated use of symmetric differences of cells.
There are many equivalent ways to define a matroid axiomatically, the most significant being in terms of: independent sets; bases or circuits; rank functions; ...