Dominating circuits in regular matroids
نویسندگان
چکیده
منابع مشابه
Dominating Circuits in Regular Matroids
In 1971, Nash-Williams proved that if G is a simple 2-connected graph on n vertices having minimum degree at least 3 (n+ 2), then any longest cycle C in G is also edge-domininating; that is, each edge of G has at least one end-vertex incident with a vertex of C. We say that a circuit C in a matroid M is dominating if each component of M/C has rank at most one. In this paper, we show that an ana...
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We consider the fundamental Matroid Theory problem of finding a circuit in a matroid spanning a set T of given terminal elements. For graphic matroids this corresponds to the problem of finding a simple cycle passing through a set of given terminal edges in a graph. The algorithmic study of the problem on regular matroids, a superclass of graphic matroids, was initiated by Gavenčiak, Král’, and...
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A cosimple regular matroid M does not have disjoint circuits if and only ifM ∈ {M(K3,3),M(Kn) (n ≥ 3)}. This extends a former result of Erdös and Pósa on graphs without disjoint circuits.
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In this paper, as an application of fuzzy matroids, the fuzzifying greedy algorithm is proposed and an achievableexample is given. Basis axioms and circuit axioms of fuzzifying matroids, which are the semantic extension for thebasis axioms and circuit axioms of crisp matroids respectively, are presented. It is proved that a fuzzifying matroidis equivalent to a mapping which satisfies the basis ...
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The purpose of this paper is to characterize all matroids M that satisfy the following minimax relation: For any nonnegative integral weight function w defined on E(M), Maximum {k : M has k circuits (repetition allowed) such that each element e of M is used at most 2w(e) times by these circuits} = Minimum {x∈X w(x) : X is a collection of elements (repetition allowed) of M such that every circui...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2014
ISSN: 0196-8858
DOI: 10.1016/j.aam.2013.10.001