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A matching in a hypergraph H is a set of pairwise disjoint hyperedges. The matching number ν ( H ) of H is the size of a maximum matching in H . A subset D of vertices of H is a dominating set of H if for every v ∈ V ∖ D there exists u ∈ D such that u and v lie in an hyperedge of H . The cardinality of a minimum dominating set of H is the domination number of H , denoted by γ ( H ) . It was proved that γ ( H ) ≤ ( r − 1 ) ν ( H ) for r -uniform hypergraphs and the 2-uniform hypergraphs (graphs) achieving equality γ ( H ) = ν ( H ) have been characterized. In this paper we generalize the inequality γ ( H ) ≤ ( r − 1 ) ν ( H ) to arbitrary hypergraph of rank r and we completely characterize the extremal hypergraphs H of rank 3 achieving equality γ ( H ) = ( r − 1 ) ν ( H ) . [ABSTRACT FROM AUTHOR]

Abstract: Let be a family of subsets of an -element set. Sperner’s theorem says that if there is no inclusion among the members of then the largest family under this condition is the one containing all -element subsets. The present paper surveys certain generalizations of this theorem. The maximum size of is to be found under the condition that a certain configuration is excluded. The configuration here is always described by inclusions. More formally, let be a poset. The maximum size of a family which does not contain as a (not-necessarily induced) subposet is denoted by . The paper is based on a lecture of the author at the Jubilee Conference on Discrete Mathematics [Banasthali University, January 11–13, 2009], but it was somewhat updated in December 2010. [Copyright &y& Elsevier]

Abstract: A nonbinary Ford sequence is a de Bruijn sequence generated by simple rules that determine the priorities of what symbols are to be tried first, given an initial word of size which is the order of the sequence being generated. This set of rules is generalized by the concept of a preference function of span , which gives the priorities of what symbols to appear after a substring of size is encountered. In this paper, we characterize preference functions that generate full de Bruijn sequences. More significantly, we establish that any preference function that generates a de Bruijn sequence of order also generates de Bruijn sequences of all orders higher than , thus making the Ford sequence no special case. Consequently, we define the preference function complexity of a de Bruijn sequence to be the least possible span of a preference function that generates this de Bruijn sequence. [Copyright &y& Elsevier]

Abstract: Formal concept analysis has been a topic of interest for about two decades. The mathematical notion of concept has its origin in formal logic. However, the empirical notion of concept has evolved through its use in many different disciplines. In this paper, we generalize the mathematical notion of concept and investigate order-theoretic properties of concept hierarchies for the new notion of concept. [Copyright &y& Elsevier]