This paper deals with the problem of the instability regions of a free-free uniform Bernoulli beam consisting of two concentrated masses at the two free ends under the follower and transversal forces as a model for a space structure. The follower force is the model for the propulsion force and the transversal force is the controller force. The main aim of this study is to analyze the effects of...

Ingleton [8, p. 123] raised the question of characterizing the class of transversal matroids that are representable over some particular field F. He noted that when F = GF(2), this problem had already been solved by de Sousa and Welsh [6] who showed that the class of binary transversal matroids coincides with the class of graphic transversal matroids. The latter class had earlier been character...

Matroids are discrete structures that capture independence under many different flavours. Our focus here is split between affine independence and transversal set theory. It was proved by Edmonds and Fulkerson in 1965 that the set of partial transversals of a set system are the independent sets of a matroid. A first attractive feature of these matroids (thus called transversal matroids) is that ...

A latin transversal in a square matrix of order n is a set of entries, no two in the same row or column, which are pairwise distinct. A longstanding conjecture of Ryser states that every Latin square with odd order has a latin transversal. Some results on the existence of a large partial latin transversal can be found in [11,6,16]. Mainly motivated by Ryser’s conjecture, Erdős and Spencer [8] p...

A set S ⊆ V of vertices in a graph G = (V,E) is called a dominating set if every vertex in V −S is adjacent to a vertex in S. A dominating set which intersects every maximum independent set in G is called an independent transversal dominating set. The minimum cardinality of an independent transversal dominating set is called the independent transversal domination number of G and is denoted by γ...

For each constant k, we present a linear time algorithm that, given a planar graph G, either finds a minimum odd cycle vertex transversal in G or guarantees that there is no transversal of size at most k.

Let m and n be integers, 2 ≤ m ≤ n. An m by n array consists of mn cells, arranged in m rows and n columns, and each cell contains exactly one symbol. A transversal of an array consists of m cells, one from each row and no two from the same column. A latin transversal is a transversal in which no symbol appears more than once. We investigte L(m, n), the largest integer such that if each symbol ...

In this tutorial paper we present a generalization of the transversal filter, called Laguerre filter, and study some of its more remarkable properties. This filter is obtained by replacing each delay of the transversal filter by a first order all-pass section, and by applying a first order low-pass filter (with the same pole used in the all-pass sections) to the filter’s input signal. Both the ...

1. Prefatory Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Several Perspectives on Transversal Matroids . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1. Set systems, transversals, partial transversals, and Hall’s theorem . . . . . . . . 2 2.2. Transversal matroids via matrix encodings of set systems . . . . . ....