A base exchange property for regular matroids
نویسنده
چکیده
In this paper, we show that for any two bases B and B of a regular matroid, there is an element e ∈ B such that there is a unique element f ∈ B for which both (B\{e}) ∪ {f} and (B\{f}) ∪ {e} are bases of M. This solves a problem posed by White in 1980.
منابع مشابه
k-Regular Matroids
The class of matroids representable over all fields is the class of regular matroids. The class of matroids representable over all fields except perhaps GF (2) is the class of near-regular matroids. Let k be a non-negative integer. This thesis considers the class of k–regular matroids, a generalization of the last two classes. Indeed, the classes of regular and near-regular matroids coincide wi...
متن کاملBase exchange properties of graphic matroids
New base exchange properties of binary and graphic matroids are derived. The graphic matroids within the class of 4-connected binary matroids are characterized by base exchange properties. Some progress with the characterization of arbitrary graphic matroids is made. Characterizing various types of matroids by base exchange properties is e.g. important in invariant theory.
متن کاملOn exchange properties for Coxeter matroids and oriented matroids
We introduce new basis exchange axioms for matroids and oriented matroids. These new axioms are special cases of exchange properties for a more general class of combinatorial structures, Coxeter matroids. We refer to them as “properties” in the more general setting because they are not all equivalent, as they are for ordinary matroids, since the Symmetric Exchange Property is strictly stronger ...
متن کاملOn Circuit Valuation of Matroids 1
The concept of valuated matroids was introduced by Dress and Wenzel as a quantitative extension of the base exchange axiom for matroids. This paper gives several sets of cryptomorphically equivalent axioms of valuated matroids in terms of (R[f 1g)-valued vectors de ned on the circuits of the underlying matroid, where R is a totally ordered additive group. The dual of a valuated matroid is chara...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 107 شماره
صفحات -
تاریخ انتشار 2014