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Circuits and Cocircuits in Regular Matroids
Graphs and Combinatorics, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Cocircuit coverings and packings for binary matroids
Mathematical Proceedings of the Cambridge Philosophical Society, 1978If M is an arbitrary loopless matroid with ground set E(M) and rank function ρ, then let α(M) be the minimum size of a set of cocircuits of M, whose union is E(M), and let β(M) be the maximum size of a set of pairwise disjoint cocircuits of M. The following conjecture is based on Gallai's theorem that the vertex-stability and vertex-covering numbers of
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Circuit-Cocircuit Reversing Systems in Regular Matroids
Annals of Combinatorics, 2008We consider that two orientations of a regular matroid are equivalent if one can be obtained from the other by successive reorientations of positive circuits and/or positive cocircuits. We study the inductive deletion-contraction structure of these equivalence classes in the set of orientations, and we enumerate these classes as evaluations of the ...
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On the intersections of circuits and cocircuits in matroids
Combinatorica, 1984A 3- or 4-element set is called a triad or a quad, respectively, if it is the intersection of a circuit and a cocircuit of a matroid. \textit{P. D. Seymour} [Combinatorica 1, 387-394 (1981; Zbl 0489.05020)] proved that a matroid has a triad if and only if it is non-binary; and then every pair of elements is contained in a triad.
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Circuits Through Cocircuits In A Graph With Extensions To Matroids
Combinatorica, 2005The circumference \(c(M)\) of a matroid \(M\) is defined to be the size of its largest circuit and the cocircumference \(c*(M)\) is the size of its largest cocircuit. Recently, Oxley posed the conjecture that for any connected matroid \(M\) with at least 2 elements, one can find a collection of at most \(c*(M)\) circuits which cover each element of \(M\
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OPTIMAL MATROID BASES: AN ALGORITHM BASED ON COCIRCUITS
The Quarterly Journal of Mathematics, 1980openaire +2 more sources
NON-SEPARATING CIRCUITS AND COCIRCUITS IN MATROIDS
2007Bráulio Maia Junior +2 more
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On the number of circuit–cocircuit reversal classes of an oriented matroid
Discrete Mathematics, 2019exaly