Fork-decompositions of matroids

For the abstract of this paper, please see the PDF file

On matroids of branch-width three

For the abstract of this paper, please see the PDF file

Improved alkaline electrochemical cell

Addition of lead ions to electrolyte suppresses zinc dendrite formation during charging cycle. A soluble lead salt can be added directly or metallic lead can be incorporated in the zinc electrode and allowed to dissolve into the electrolyte

On minor-minimally-connected matroids

AbstractBy a well-known result of Tutte, if e is an element of a connected matroid M, then either the deletion or the contraction of e from M is connected. If, for every element of M, exactly one of these minors is connected, then we call M minor-minimally-connected. This paper characterizes such matroids and shows that they must contain a number of two-element circuits or cocircuits. In addition, a new bound is proved on the number of 2-cocircuits in a minimally connected matroid

On a matroid identity

The purpose of this note is to prove an identity for generalized Tutte-Grothendieck invariants, at least two special cases of which have already proved to be of considerable use. In addition, one of these special cases is used to strengthen results of Lindström on the critical exponent of a representable matroid and the chromatic number of a regular matroid. © 1983

On a packing problem for infinite graphs and independence spaces

In this paper several infinite extensions of the well-known results for packing bases in finite matroids are considered. A counterexample is given to a conjecture of Nash-Williams on edge-disjoint spanning trees of countable graphs, and a sufficient condition is proved for the packing problem in independence spaces over a countably infinite set. © 1979

On ternary transversal matroids

AbstractThe purpose of this paper is to answer a question of Ingleton by characterizing the class of ternary transversal matroids

On the Numbers of Bases and Circuits in Simple Binary Matroids

Quirk and Seymour have shown that a connected simple graph has at least as many spanning trees as circuits. This paper extends and strengthens their result by showing that in a simple binary matroid M the quotient of the number of bases by the number of circuits is at least 2. Moreover, if M has no coloops and rank r, this quotient exceeds 6(r + 1)/19. © 1983, Academic Press Inc. (London) Limited. All rights reserved

The Cable-Telco Cross-Ownership Prohibition: First Amendment Infringement Through Obsolescence

Since 1970, the FCC has prohibited all telephone companies from providing video programming in their local service areas. The primary rationale behind this prohibition was to promote the cable industry. Since 1984, however, the cable industry has seen tremendous growth with very little competition. New technology and market demands have now necessitated a reevaluation of the ban on cable-telco cross-ownership. The Author argues that with the changes that have occurred in the marketplace, the ban is now both an invalid prior restraint and an infringement on commercial expression and thus a violation of the First Amendment rights of telephone companies. In addition, he claims that an open and competitive cable marketplace would promote development of the United States telecommunications infrastructure