A clique-transversal set S of a graph G is a set of vertices of G such that S meets all cliques of G. The clique-transversal number, denoted τc(G), is the minimum cardinality of a clique-transversal set in G. In this paper we present an upper bound and a lower bound on τc(G) for cubic graphs, and characterize the extremal cubic graphs achieving the lower bound. In addition, we present a sharp u...

Let G = (V, E) be a graph with chromatic number χ(G). A dominating set D of G is called a chromatic transversal dominating set (ctd-set) if D intersects every color class of every χ-partition of G. The minimum cardinality of a ctd-set of G is called the chromatic transversal domination number of G and is denoted by γct(G). In this paper we characterize the class of trees, unicyclic graphs and c...

Let A be an m n matrix in which the entries of each row are all distinct. Drisko 4] showed that, if m 2n ? 1, then A has a transversal: a set of n distinct entries with no two in the same row or column. We generalize this to matrices with entries in a matroid. For such a matrix A, we show that if each row of A forms an independent set, then we can require the transversal to be independent as we...

Contractile properties of skeletal muscle are studied for various purposes and mainly by means of force or torque twitch responses. This study compared contractile properties estimated from isometric longitudinal and transversal vastus lateralis twitch mechanical actions using torque and tensiomyography (TMG) as assessment methods, respectively. We calculated delay, contraction, sustain, half r...

The study of gene functions requires the development of a DNA library of high quality through much of testing and screening. Pooling design is a mathematical tool to reduce the number of tests for DNA library screening. The transversal design is a special type of pooling design, which is good in implementation. In this paper, we present a new construction for transversal designs. We will also e...

The standard Pirogov–Sinai theory is generalized to the class of models with two modes of interaction: longitudinal and transversal. Under rather general assumptions about the longitudinal interaction and for one specific form of the transversal interaction it is proved that such system has a variety of phase transitions at any temperature: the parameter which plays the role of inverse temperat...

In this work we consider the problem of finding a minimum Ck-transversal (a subset of vertices hitting all the induced chordless cycles with k vertices) in a graph with bounded maximum degree. In particular, we seek for dichotomy results as follows: for a fixed value of k, finding a minimum Ck-transversal is polynomial-time solvable if k ≤ p, and NP -hard otherwise.

We establish some inequalities about the Khovanov-Rozansky cohomologies of braids. These give new upper bounds of the self-linking numbers of transversal links in standard contact S which is sharper than the well known bound given by the HOMFLY polynomial. We also introduce a sequence of transversal link invariants, and discuss some of their properties.

We show that if a line ` is an isolated line transversal to a finite familyF of (possibly intersecting) balls inR and no two balls are externally tangent on ` then there is a subset G ⊆ F of size at most 12 such that ` is an isolated line transversal to G. We generalize this result to families of semi-algebraic ovaloids.

A k-plex in a latin square of order n is a selection of kn entries that includes k representatives from each row and column and k occurrences of each symbol. A 1-plex is also known as a transversal. It is well known that if n is even then Bn, the addition table for the integers modulo n, possesses no transversals. We show that there are a great many latin squares that are similar to Bn and have...