Rank-Three Matroids are Rayleigh

نویسنده

  • David G. Wagner
چکیده

A Rayleigh matroid is one which satisfies a set of inequalities analogous to the Rayleigh monotonicity property of linear resistive electrical networks. We show that every matroid of rank three satisfies these inequalities.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

An 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 کامل

Some minimal non - orientable matroids of rank three by Günter M . Ziegler

We construct an infinite family of minor-minimal rank three matroids that are not orientable.

متن کامل

Weak orientability of matroids and polynomial equations

This paper studies systems of polynomial equations that provide information about orientability of matroids. First, we study systems of linear equations over F2, originally alluded to by Bland and Jensen in their seminal paper on weak orientability. The Bland-Jensen linear equations for a matroid M have a solution if and only if M is weakly orientable. We use the Bland-Jensen system to determin...

متن کامل

Rayleigh Matroids

Motivated by a property of linear resistive electrical networks, we introduce the class of Rayleigh matroids. These form a subclass of the balanced matroids defined by Feder and Mihail [10] in 1992. We prove a variety of results relating Rayleigh matroids to other well–known classes – in particular, we show that a binary matroid is Rayleigh if and only if it does not contain S8 as a minor. This...

متن کامل

Query Lower Bounds for Matroid Intersection

We consider the number of queries needed to solve the matroid intersection problem, a question raised by Welsh (1976). Given two matroids of rank r on n elements, it is known that O(nr) independence queries suffice. Unfortunately, very little is known about lower bounds for this problem. This paper describes three lower bounds which, to our knowledge, are the best known: 2n− 2 queries are neede...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Electr. J. Comb.

دوره 12  شماره 

صفحات  -

تاریخ انتشار 2005