For a presentation A of a transversal matroid M , we study the ordered set TA of single-element transversal extensions of M that have presentations that extend A; extensions are ordered by the weak order. We show that TA is a distributive lattice, and that each finite distributive lattice is isomorphic to TA for some presentation A of some transversal matroid M . We show that TA ∩ TB, for any t...

Let k, d, λ > 1 be integers with d > λ and let X ⊂ R be a finite set. A (d−λ)-plane L transversal to the convex hull of all k-sets of X is called Kneser transversal. If in addition L contains (d− λ) + 1 points of X, then L is called complete Kneser transversal. In this paper, we present various results on the existence of (complete) Kneser transversals for λ = 2, 3. In order to do this, we intr...

The NP-complete problem Feedback Vertex Set is that of deciding whether or not it is possible, for a given integer k ≥ 0, to delete at most k vertices from a given graph so that what remains is a forest. The variant in which the deleted vertices must form an independent set is called Independent Feedback Vertex Set and is also NP-complete. In fact, even deciding if an independent feedback verte...

In sec tion 1, transversal Inatroids are assoc iated with "syste ms of di s tinct represe ntatives" (i. e., tra nsversals) and,. more generally , matc hing matroids are associated with matc hings in graphs . Th e transversal matrolds and a theore m of P. J. Higgins on disjoint transversals of a famil y of se ts , along wIth th e well-known graphIc matrold s a nd some theorems on decomposition o...

As plant fibres are increasingly used in technical textiles and their composites, underlying principles of wound healing in living plant fibres are relevant to product quality, and provide inspiration for biomimetic healing in synthetic materials. In this work, two Linum usitatissimum cultivars differing in their stem mechanical properties, cv. Eden (stems resistant to lodging) and cv. Drakkar ...

A hypergraph H = (V,E) is a subtree hypergraph if there is a tree T on V such that each hyperedge of E induces a subtree of T . To find a minimum size transversal for a subtree hypergraph is, in general, NP-hard. In this paper, we show that if it is possible to decide if a set of vertices W ⊆ V is a transversal in time S(n) ( where n = |V | ), then it is possible to find a minimum size transver...

Let G be a graph with maximum degree ∆ whose vertex set is partitioned into parts V (G) = V1∪ . . .∪Vr . A transversal is a subset of V (G) containing exactly one vertex from each part Vi. If it is also an independent set, then we call it an independent transversal. The local degree of G is the maximum number of neighbors of a vertex v in a part Vi, taken over all choices of Vi and v 6∈ Vi. We ...

Gastrointestinal form is the second stage of acute radiation syndrome (ARS) with a threshold dose of 8 Gy in man. It represents an absolutely lethal clinical-pathological unit, necro-hemorrhagic enteritis and proctocolitis, with unknown causal therapy. Elk-1 is a protein acting as a transcription factor activating specified genes. The purpose of our study was to examine the expression of phosph...

Given a finite set V , and a hypergraph H ⊆ 2 , the hypergraph transversal problem calls for enumerating all minimal hitting sets (transversals) for H. This problem plays an important role in practical applications as many other problems were shown to be polynomially equivalent to it. Fredman and Khachiyan (1996) gave an incremental quasi-polynomial time algorithm for solving the hypergraph tra...

OBJECTIVE The aim of the present study was to compare dentoalveolar changes in mandibular arch, regarding transversal measures and buccal bone thickness, in patients undergoing the initial phase of orthodontic treatment with self-ligating or conventional bracket systems. METHODS A sample of 25 patients requiring orthodontic treatment was assessed based on the bracket type. Group 1 comprised 1...