We show that there exists a bipartite graph containing n matchings of sizes mi n satisfying ∑ i mi = n 2 + n/2 − 1, such that the matchings have no rainbow matching. This answers a question posed by Aharoni, Charbit and Howard. We also exhibit (n − 1) × n latin rectangles that cannot be decomposed into transversals, and some related constructions. In the process we answer a question posed by Hä...

Let k, d, λ > 1 be integers with d > λ. Let m(k, d, λ) be the maximum positive integer n such that every set of n points (not necessarily in general position) in R has the property that the convex hulls of all k-sets have a common transversal (d − λ)-plane. It turns out that m(k, d, λ) is strongly connected with other interesting problems, for instance, the chromatic number of Kneser hypergraph...

We are seeking a sufficient condition that forces a transversal in a generalized Latin square. A generalized Latin square of order n is equivalent to a proper edge-coloring of Kn,n. A transversal corresponds to a multicolored perfect matching. Akbari and Alipour defined l(n) as the least integer such that every properly edge-colored Kn,n, which contains at least l(n) different colors, admits a ...

We prove that every tournament T with no three disjoint cycles contains a set X of at most four vertices such that T −X is acyclic.

An odd neighborhood transversal of a graph is a set of its vertices that intersects the set of neighbors of each of its vertices in an odd number of elements. In the case of grid graphs this odd number will be either one or three. We characterize those grid graphs that have odd neighborhood transversals.

In this paper, we consider two methods for computing lower cover of elements in closure systems for which we know an implicational basis: intersecting meet-irreducible elements or computing minimal transversals of sets of minimal generators. We provide experimental results on the runtimes for single computations of lower covers and depth-first searches.

We extend the classical Stallings theory (describing subgroups of free groups as automata) to direct products and abelian groups: after introducing enriched automata (i.e., with extra labels), we obtain an explicit bijection between a certain type such automata, which - it happens in group is computable finitely generated case. This approach provides neat geometric description (even non gener...

We give some theorems of bi-Lipschitz or C sufficiency of jets which are expressed by means of transversality with respect to some strata of a stratification satisfying the (L) condition of T. Mostowski. This enables us to prove that the number of metric types of intersection of smooth transversals to a stratum of an (a) regular stratification of a subanalytic set is finite.

In this paper some results on the topology of the space of k-flats in Rn are proved, similar to the Borsuk-Ulam theorem on coverings of sphere. Some corollaries on common transversals for families of compact sets in Rn, and on measure partitions by hyperplanes, are deduced.

We study the problem of bounding from above and below a given set of bit vectors by the set of satisfying truth assignments of a Horn formula. We point out a rather unexpected connection between the upper bounding problem and the problem of generating all transversals of a hypergraph, and settle several related complexity questions.