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 کاملMatroids and Graphs with Few Non-Essential Elements
An essential element of a 3–connected matroid M is one for which neither the deletion nor the contraction is 3–connected. Tutte’s Wheels and Whirls Theorem proves that the only 3–connected matroids in which every element is essential are the wheels and whirls. In an earlier paper, the authors showed that a 3–connected matroid with at least one non-essential element has at least two such element...
متن کاملMatroids and graphs with few non-essential edges
Finally, Theorem 1.2 is quite straightforward to deduce from Corollary 5.4. Alternatively , it is not diicult to prove this theorem directly using Theorem 2.1. We conclude by presenting the rst of these proofs. Proof of Theorem 1.2. From the list given in Corollary 5.4 of binary 3{connected matroids whose set of non-essential elements has rank two, we eliminate the ma-troids under (i) and (iii)...
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 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...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2006
ISSN: 0012-365X
DOI: 10.1016/j.disc.2005.10.029