Largest circuits in matroids
نویسندگان
چکیده
منابع مشابه
BASES AND CIRCUITS OF FUZZIFYING MATROIDS
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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متن کاملSpanning Circuits in Regular Matroids
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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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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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2005
ISSN: 0196-8858
DOI: 10.1016/j.aam.2004.09.002