In the hitting set problem one is given m subsets of a nite set N and one has to nd an X N of minimum cardinality that hits intersects all of them The problem is NP hard It is not known whether there exists a polynomial time approximation algorithm for the hitting set problem with a nite performance ratio Special cases of the hitting set problem are described for which nite performance ratios a...

In the hitting set problem one is given m subsets of a nite set N and one has to nd an X N of minimum cardinality that \hits" (intersects) all of them. The problem is NP-hard. It is not known whether there exists a polynomial-time approximation algorithm for the hitting set problem with a nite performance ratio. Special cases of the hitting set problem are described for which nite performance r...

Oxidation of NH3/n-heptane mixtures at pressures up to 100 atm and temperatures 400–900 K was characterized experimentally in a laminar flow reactor jet-stirred reactor. A detailed chemical kinetic model developed, updating the hydrogen amine subsets introducing subset for coupling with emphasis on NH2+n-heptane reaction. The provided good prediction ignition delay times measured rapid compress...

Let F be a family of subsets of an n-element set. Sperner’s theorem says that if there is no inclusion among the members of F then the largest family under this condition is the one containing all bn2 celement subsets. The present paper surveys certain generalizations of this theorem. The maximum size of F is to be found under the condition that a certain configuration is excluded. The configur...

Composition problem is considered for partition constrained vertex subsets of n dimensional unit cube n E . Generating numerical characteristics of n E subsets partitions is considered by means of the same characteristics in 1 − n dimensional unit cube, and construction of corresponding subsets is given for a special particular case. Using pairs of lower layer characteristic vectors for 1 − n E...

If D (V, A) is a digraph, its p-competition graph for p a positive integer has vertex set V and an edge between x and y if and only if there are distinct vertices a, , a n in D with (x, a and (y, a) arcs of D for each 1, , p. This notion generalizes the notion of ordinary competition graph, which has been widely studied and is the special case where p 1. Results about the case where p 2 are obt...

Let H denote the set {f1, f2, ..., fn}, 2 the collection of all subsets of H and F ⊆ 2 be a family. The maximum of |F| is studied if any k subsets have a non-empty intersection and the intersection of any l distinct subsets (1 ≤ k < l) is empty. This problem is reduced to a covering problem. If we have the conditions that any two subsets have a non-empty intersection and the intersection of any...

In the last few years, a number of metrics and methods have been introduced for studying the relative “importance” of nodes within complex network structures [6]. Among these metrics, k-core decomposition is a well-established method for identifying particular subsets of the graph called k-cores, or k-shells [7]. Informally, a k-core is obtained by recursively removing all nodes of degree small...

The dimension D(S) of a family S of subsets of n = (1,2, . . . . n> is defined as the minimum number of permutations of n such that every A E S is an intersection of initial segments of the permutations. Equivalent characterizations of D(S) are given in terms of suitable arrangements, interval dimension, order dimension, and the chromatic number of an associated hypergraph. We also comment on t...