A link between matroid theory and p-branes is discussed. The Schild type action for p-branes and matroid bundle notion provide the two central structures for such a link. We use such a connection to bring the duality concept in matroid theory to p-branes physics. Our analysis may be of particular interest in M-theory and in matroid bundle theory.

Induction (or transformation) by bipartite graphs is one of the most important operations on matroids, and it is well known that the induction of a matroid by a bipartite graph is again a matroid. As an abstract form of this fact, the induction of a matroid by a linking system is known to be a matroid. M-convex functions are quantitative extensions of matroidal structures, and they are known as...

An element e of a 3-connected matroid M is said to be contractible provided that M/e is 3-connected. In this paper, we show that a 3-connected matroid M with exactly k contractible elements has at least max { r(M) + 6− 2k 4 , |E(M)| + 6− 3k 5 } triangles. For each k, we construct an infinite family of matroids that attain this bound. New sharp bounds for the number of triads of a minimally 3-co...

Let A = An,m,k be a random n × m matrix over GF2 where each column consists of k randomly chosen ones. Let M be an arbirary fixed binary matroid. We show that if m/n and k are sufficiently large then as n → ∞ the binary matroid induced by A contains M as a minor.

In this paper, we obtain a forbidden minor characterization of a cographic matroid M for which the splitting matroid Mx,y is graphic for every pair x, y of elements of M .

We propose a new approach for speeding up enumeration algorithms. The approach does not rely on data structures deeply, instead utilizes analysis of computation time. It speeds enumeration algorithms for directed spanning trees, matroid bases, and some bipartite matching problems. We show one of these improved algorithms: one for enumerating matroid bases. For a given matroid M with m elements ...

Blocks of a matroid are called hyperplanes. For various definitions and results connected with matroids, see [26]. Subsets of X , which are intersections of hyperplanes are called flats of a matroid. Each subset Y c_ X has a well-defined rank. If F is a flat of rank i and x e X \ F , then, there is a unique flat of rank (i + 1) which contains FU{x}. Rank of X is said to be the rank of matroid. ...

Let K̃3,n, n ≥ 3, be the simple graph obtained from K3,n by adding three edges to a vertex part of size three. We prove that if H is a hyperplane of a 3-connected matroid M and M 6∼= M∗(K̃3,n), then there is an element x in H such that the simple matroid associated with M/x is 3-connected.

By combining the concepts of graviton and matroid, we outline a new gravitational theory which we call gravitoid theory. The idea of this theory emerged as an attempt to link the mathematical structure of matroid theory with M-theory. Our observations are essentially based on the formulation of matroid bundle due to MacPherson and Anderson-Davis. Also, by considering the oriented matroid theory...

This paper presents a theorem concerning a matroid with the parity condition. The theorem provides matroid generalizations of graph-theoretic results of Lewin [3] and Gallai [1]. Let M=(E, F) be a matroid, where E is a finite set of elements and F is the family of independent sets of M (in this paper, we presuppose a knowledge of matroid theory; our standard reference is Welsh [4]). Assume that...