Results 141 to 150 of about 511 (171)

k-Best constrained bases of a matroid

Zeitschrift Fuer Operations-Research, Serie B: Praxis, 1990
Summary: We propose a method for finding a set of k-best bases of an arbitrary matroid where the bases are required to satisfy additional partitionlike constraints. An application of this problem is discussed.
F Rendl
exaly   +5 more sources

Determination of the bases of a splitting matroid

European Journal of Combinatorics, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
M. M. Shikare, Ghodratollah Azadi
exaly   +4 more sources

Weight distribution of the bases of a binary matroid

Applied Mathematics Letters, 1998
Let M be a weighted binary matroid and w1 < … < wm be the increasing sequence of all possible distinct weights of bases of M. We give a sufficient condition for the property that w1, …, wm is an arithmetical progression of common difference d.
Zhou, S, Zhou, S.
exaly   +2 more sources

Complementary bases of a matroid

Discrete Mathematics, 1974
Let e"1, e'"1, e"2, e'"2, ..., e"n, e'"n be the elements of matroid M. Suppose that {e"1, e"2, ...;, e"n} is a base of M and that every circuit of M contains at least m + 1 elements. We prove that there exist at least 2^m bases, called complementary bases, of M with the property that only one of each complementary pair e"j, e'"j is contained in any ...
exaly   +2 more sources

Characterization of removable elements with respect to having k disjoint bases in a matroid

Discrete Applied Mathematics, 2012
The well-known spanning tree packing theorem of Nash-Williams and Tutte characterizes graphs with k edge-disjoint spanning trees. Edmonds generalizes this theorem to matroids with k disjoint bases.
Hong-Jian Lai, Yanting Liang
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Bases in Infinite Matroids

Journal of the London Mathematical Society, 1991
Summary: We consider bases in matroids of infinite rank, and prove: (a) the existence of a perfect matching in the `transition graph' of any two bases. This is an extension of the existence of a non-zero generalized diagonal in the transition matrix between bases in finite dimensional linear spaces, and settles a conjecture of the second author [Math ...
Aharoni, Ron, Pouzet, Maurice
openaire   +2 more sources

Interdiction of minimum spanning trees and other matroid bases

Mathematical Programming
In the minimum spanning tree (MST) interdiction problem, we are given a graph $G=(V,E)$ with edge weights, and want to find some $X\subseteq E$ satisfying a knapsack constraint such that the MST weight in $(V,E\setminus X)$ is maximized. Since MSTs of $G$
Noah Weninger, Ricardo Fukasawa, Fukasawa Ricardo   +2 more
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Improved bound for the Carathéodory rank of the bases of a matroid

Journal of Combinatorial Theory Series B, 2003
Let M be a matroid on m elements and let r be its rank. We show that any vector in the integer cone of the incidence vectors of bases of M can be written as nonnegative integer combination of at most m+r−1 incidence vectors of bases of ...
Soares, José, José Soares, José Coelho de Pina, de Pina, José Coelho   +3 more
exaly   +2 more sources

On the Number of Bases of Bicircular Matroids

Annals of Combinatorics, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Giménez, Omer, de Mier, Anna, Noy, Marc
openaire   +1 more source

Matroid-Based Packing of Arborescences

SIAM Journal on Discrete Mathematics, 2013
We provide the directed counterpart of a slight extension of Katoh and Tanigawa's result [SIAM J. Discrete Math., 27 (2013), pp. 155--185] on rooted-tree decompositions with matroid constraints. Our result characterizes digraphs having a packing of arborescences with matroid constraints.
Durand de Gevigney, Olivier, Nguyen, Viet-Hang, Szigeti, Zoltán   +2 more
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