نتایج جستجو برای: matroid theory

تعداد نتایج: 784247  

2015
KARIM ADIPRASITO ERIC KATZ

The matroid is called loopless if the empty subset of E is closed, and is called a combinatorial geometry if in addition all single element subsets of E are closed. A closed subset of E is called a flat of M, and every subset of E has a well-defined rank and corank in the poset of all flats of M. The notion of matroid played a fundamental role in graph theory, coding theory, combinatorial optim...

Journal: :CoRR 2013
Bin Yang William Zhu

In mathematics and computer science, connectivity is one of the basic concepts of matroid theory: it asks for the minimum number of elements which need to be removed to disconnect the remaining nodes from each other. It is closely related to the theory of network flow problems. The connectivity of a matroid is an important measure of its robustness as a network. Therefore, it is very necessary ...

Journal: :Journal of Computational Biology 2015

2005
Joseph E. Bonin

Matroid theory is a combinatorial abstraction of geometry, with flats playing the role of subspaces. Cyclic flats are special flats that contain key geometric information about a matroid. This talk presents a variety of recent results and open problems about the lattice of cyclic flats. In particular, we show that every finite lattice arises as the lattice of cyclic flats of a (fundamental tran...

Journal: :CoRR 2016
Petr Hlinený

Path-width of matroids naturally generalizes better known path-width of graphs, and is NP-hard by a reduction from the graph case. While the term matroid path-width was formally introduced by Geelen–Gerards–Whittle [JCTB 2006] in pure matroid theory, it was soon recognized by Kashyap [SIDMA 2008] that it is the same concept as long-studied so called trellis complexity in coding theory, later na...

Journal: :Discrete Applied Mathematics 2016
Csongor Gy. Csehi András Recski

Graphic matroids form one of the most significant classes in matroid theory. When introducing matroids, Whitney concentrated on relations to graphs. The definition of some basic operations like deletion, contraction and direct sum were straightforward generalizations of the respective concepts in graph theory. Most matroid classes, for example those of binary, regular or graphic matroids, are c...

Journal: :Int. J. Machine Learning & Cybernetics 2014
Qingyin Li William Zhu

Rough sets are efficient for data pre-processing in data mining. Matroids are based on linear algebra and graph theory, and have a variety of applications in many fields. Both rough sets and matroids are closely related to lattices. For a serial and transitive relation on a universe, the collection of all the regular sets of the generalized rough set is a lattice. In this paper, we use the latt...

2006
Petr Hlinený

In this paper we look at complexity aspects of the following problem (matroid representability) which seems to play an important role in structural matroid theory: Given a rational matrix representing the matroid M , the question is whether M can be represented also over another specific finite field. We prove this problem is hard, and so is the related problem of minor testing in rational matr...

2002
SANTOSH N. KABADI

In [7, 10], the concept of pseudomatroid was developed as a proper generalization of the concept of matroid. The same concept was independently developed as ∆-matroid in [4, 5]. Throughout the paper, we use the more popular name ∆-matroid for this structure. In [6], the concept of ∆-matroid was further generalized to jump system. Further interesting results on jump system are reported in [1, 3,...

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