Given G = (V,E) an undirected graph with matching number ν(G), we define d-blockers as subsets of edges B such that ν(G′ = (V,E \B)) ≤ ν(G)−d. We define d-transversals T as subsets of edges such that every maximum matchingM has |M ∩T | ≥ d. We explore connections between d-blockers and d-transversals. Special classes of graphs are examined which include complete graphs, regular bipartite graphs...

We focus on the maximum number of minimal transversals in 3-partite 3-uniform hypergraphs n vertices. Those (and their transversals) are commonly found database applications. In this paper we prove that grows at least like 1.4977^n and most 1.5012^n.

Poisson transversals are submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In this communication, we prove a normal form theorem for Poisson maps around Poisson transversals. A Poisson map pulls a Poisson transversal back to a Poisson transversal, and our first main result states that simultaneous normal forms exist around such transversa...

A latin square of order n is an n×n array of n symbols in which each symbol occurs exactly once in each row and column. A transversal of such a square is a set of n entries such that no two entries share the same row, column or symbol. Transversals are closely related to the notions of complete mappings and orthomorphisms in (quasi)groups, and are fundamental to the concept of mutually orthogon...

A transversal of a hypergraph is a set of vertices intersecting each hyperedge. We design and analyze new exponential-time algorithms to enumerate all inclusion-minimal transversals of a hypergraph. For each fixed k ≥ 3, our algorithms for hypergraphs of rank k, where the rank is the maximum size of a hyperedge, outperform the previous best. This also implies improved upper bounds on the maximu...

As the real common generalisations of both orthodox transversals and adequate in abundant semigroups, concept refined generalised quasi-adequate transversals, briefly, RGQA was introduced by Kong Wang. In this paper, for transversal, necessary sufficient condition sets I ? to be bands is investigated. It demonstrated that are if only transversal weakly simplistic. Moreover, So being simplistic ...

We state and prove a theorem (Theorem 1 below) which strengthens previously known results concerning disjoint common partial transversals of two families of sets. This theorem may be viewed as a result on transversal pre-independence structures. We define a "disjoint-exchange structure" on a set and extend the result to such structures (Theorem 3 below). Then we give an application of this theo...

Transversals in r-partite graphs with various properties are known to have many applications in graph theory and theoretical computer science. We investigate f -bounded transversals (or f -BT), that is, transversals whose connected components have order at most f . In some sense we search for the the sparsest f -BT-free graphs. We obtain estimates on the smallest maximum degree that 3-partite a...

Let L be the space of line transversals to a nite family of pairwise disjoint compact convex sets in R 3. We prove that each connected component of L can itself be represented as the space of transversals to some nite family of pairwise disjoint compact convex sets.