منابع مشابه
Basis-Transitive Matroids
We consider the problem of classifying all finite basis-transitive matroids and reduce it to the classification of the finite basis-transitive and point-primitive simple matroids (or geometric lattices, or dimensional linear spaces). Our main result shows how a basisand point-transitive simple matroid is decomposed into a so-called supersum. In particular each block of imprimitivity bears the s...
متن کاملRota's Basis Conjecture for Paving Matroids
Rota conjectured that, given n disjoint bases of a rank-n matroid M , there are n disjoint transversals of these bases that are all bases of M . We prove a stronger statement for the class of paving matroids.
متن کاملBasis-exchange Properties of Sparse Paving Matroids
It has been conjectured that, asymptotically, almost all matroids are sparse paving matroids. We provide evidence for five long-standing, basis-exchange conjectures by proving them for this large class of matroids. To Geoff Whittle on his 60th birthday
متن کاملOn basis-exchange properties for matroids
We give a counterexample to a conjecture by Wild about binary matroids. We connect two equivalent lines of research in matroid theory: a simple type of basis-exchange property and restrictions on the cardinalities of intersections of circuits and cocircuits. Finally, we characterize direct sums of series-parallel networks by a simple basis-exchange property. In [9], Wild proposed a characteriza...
متن کاملBasis graphs of even Delta-matroids
A -matroid is a collection B of subsets of a finite set I, called bases, not necessarily equicardinal, satisfying the symmetric exchange property: For A,B ∈ B and i ∈ A B, there exists j ∈ B A such that (A {i, j}) ∈ B. A -matroid whose bases all have the same cardinality modulo 2 is called an even -matroid. The basis graph G=G(B) of an even -matroid B is the graph whose vertices are the bases o...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1978
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1978-0500521-5