منابع مشابه
The Erdös-Pósa property for matroid circuits
The number of disjoint cocircuits in a matroid is bounded by its rank. There are, however, matroids with arbitrarily large rank that do not contain two disjoint cocircuits; consider, for example, M(Kn) and Un,2n. Also the bicircular matroids B(Kn) have arbitrarily large rank and have no 3 disjoint cocircuits. We prove that for each k and n there exists a constant c such that, if M is a matroid ...
متن کاملAn Extension of Matroid Rank Submodularity and the Z-Rayleigh Property
We define an extension of matroid rank submodularity called R-submodularity, and introduce a minor-closed class of matroids called extended submodular matroids that are well-behaved with respect to R-submodularity. We apply R-submodularity to study a class of matroids with negatively correlated multivariate Tutte polynomials called the Z-Rayleigh matroids. First, we show that the class of exten...
متن کاملRelaxations of the matroid axioms I: Independence, Exchange and Circuits
Motivated by a question of Duval and Reiner about higher Laplacians of simplicial complexes, we describe various relaxations of the defining axioms of matroid theory to obtain larger classes of simplicial complexes that contain pure shifted simplicial complexes. The resulting classes retain some of the matroid properties and allow us to classify matroid properties according to the relevant axio...
متن کاملConvexity and Steinitz's Exchange Property
Convex analysis” is developed for functions defined on integer lattice points. We investigate the class of functions which enjoy a variant of Steinitz’s exchange property. It includes linear functions on matroids, valuations on matroids (in the sense of Dress and Wenzel), and separable concave functions on the integral base polytope of submodular systems. It is shown that a function ω has the S...
متن کاملInsecure Property and the Efficiency of Exchange*
We examine the effect of insecure property and its accompanying enforcement costs on the ef®ciency of exchange. Because of the large enforcement costs that may be induced by the expectation of exchange, limited settlement without exchange may be ex ante superior for an adversary or even Pareto dominant. We therefore show how the removal of restrictions on exchange and the development of secure ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1995
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00071-3