منابع مشابه
On Disjoint Common Bases in Two Matroids
We prove two results on packing common bases of two matroids. First, we show that the computational problem of common base packing reduces to the special case where one of the matroids is a partition matroid. Second, we give a counterexample to a conjecture of Chow, which proposed a sufficient condition for the existence of a common base packing. Chow’s conjecture is a generalization of Rota’s ...
متن کاملDisjoint Bases for a Countable Family of Rank-finite Matroids
Let M = (Mr)reW be a system of matroids on a set S. For every transfinite sequence / of distinct elements of 5, we define a number TJ(/). In [12] we proved that the condition that r](f) 3=0 for every possible choice of/is necessary for M to have a system of mutually disjoint bases. Further, we showed that this condition is sufficient if R is countable and Mr is a rank-finite transversal matroid...
متن کاملBases in Infinite Matroids
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 [8]. (b) A Cantor-Bernstein theorem for matroids. (c) The e...
متن کاملBASES 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 ...
متن کاملRegular matroids without disjoint circuits
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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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2011
ISSN: 0895-4801,1095-7146
DOI: 10.1137/100815232