Results 11 to 20 of about 511 (171)
The lattices of matroid bases and exact matroid bases
Archiv der Mathematik, 1991 Combinatorial objects are often associated with the polytope generated by the incidence vectors of the objects. The lattice of these incidence vectors is the set of all of their integer combinations. Such lattices are described if the objects are the bases of a matroid on \(E\), or only those bases which contain exactly \(p\) elements of a given subset
Rieder, Jörg
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SIAM Journal on Discrete Mathematics, 2023 Recently, it was proved by Bérczi and Schwarcz that the problem of factorizing a matroid into rainbow bases with respect to a given partition of its ground set is algorithmically intractable. On the other hand, many special cases were left open. We first show that the problem remains hard if the matroid is graphic, answering a question of Bérczi and ...
Florian Hörsch +2 more
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A characterization of the base-matroids of a graphic matroid
Contributions to Discrete Mathematics, 2010 Let M=(E,F) be a matroid on a set E and B one of its bases. A closed set θ⊆E is saturated with respect to B when |θ∩B|≤r(θ), where r(θ) is the rank of θ. The collection of subsets I of E such that |I∩θ|≤r(θ) for every closed saturated set θ turns out to be the family of independent sets of a new matroid on E, called base-matroid and denoted by MB.
MAFFIOLI, FRANCESCO, ZAGAGLIA, NORMA
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Bounding the number of bases of a matroid
Combinatorica, 1995 The possibility of bounding the number of bases of a matroid by a polynomial of the size \(k\) of the underlying set, or by a polynomial of the size of \(k\) times the number of circuits, is investigated. The latter holds for every member of a minor closed class of matroids if and only if the class does not contain the direct sum of an arbitrarily ...
Ding, Guoli
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Problems on Group-Labeled Matroid Bases [PDF]
CoRRConsider a matroid equipped with a labeling of its ground set to an abelian group. We define the label of a subset of the ground set as the sum of the labels of its elements. We study a collection of problems on finding bases and common bases of matroids with restrictions on their labels.
Hörsch, Florian +4 more
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Matroid bases with cardinality constraints on the intersection. [PDF]
Math Program, 2022 AbstractGiven two matroids $$\mathcal {M}_{1} = (E, \mathcal {B}_{1})$$ M 1 = ( E , B
Lendl S, Peis B, Timmermans V.
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All your bases are belong to us : listing all bases of a matroid by greedy exchanges [PDF]
, 2022 You provide us with a matroid and an initial base. We say that a subset of the bases "belongs to us" if we can visit each one via a sequence of base exchanges starting from the initial base. It is well-known that "All your base are belong to us".
Mutze, Torsten +2 more
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Matroid intersection, base packing and base covering for infinite matroids [PDF]
Combinatorica, 2014 As part of the recent developments in infinite matroid theory, there have been a number of conjectures about how standard theorems of finite matroid theory might extend to the infinite setting. These include base packing, base covering, and matroid intersection and union.
Nathan J. Bowler, Johannes Carmesin
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Monotone Submodular Maximization over a Matroid via Non-Oblivious Local Search [PDF]
, 2013 We present an optimal, combinatorial 1−1/e approximation algorithm for monotone submodular optimization over a matroid constraint. Compared to the continuous greedy algorithm (Calinescu, Chekuri, Pál and Vondrák, 2008), our algorithm is extremely simple ...
Filmus, Yuval +3 more
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Structures of Cycle Bases with Some Extremal Properties [PDF]
, 2014 In this paper, authors investigate the structures of cycle bases with extremal properties which are related with map geometries, i.e., Smarandache 2-dimensional manifolds.
Han, Ren, Yun Bai, Han Ren, Bai, Yun
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