Given a hypergraph $\mathcal {H} $, the dual hypergraph of $\mathcal {H} $ is the
hypergraph of all minimal transversals of $\mathcal {H} $. The dual hypergraph is always …

A graph class is said to be tame if graphs in the class have a polynomially bounded number
of minimal separators. Tame graph classes have good algorithmic properties, which follow …

Using a new matrix analysis tool, called semi-tensor product of matrices (STP) developed in
recent years, this paper investigates the problem of finding control sets (or dominating sets) …

Minimal separators in graphs are an important concept in algorithmic graph theory. In
particular, many problems that are NP-hard for general graphs are known to become …

A hypergraph is said to be 1‐Sperner if for every two hyperedges the smallest of their two set
differences is of size one. We present several applications of 1‐Sperner hypergraphs to …

An efficient routing using a virtual backbone (VB) network is one of the most significant
improvements in the wireless sensor network (WSN). One promising method for selecting …

In this paper we prove that the dominator chromatic number of every oriented tree is
invariant under reversal of orientation. In addition to this marquee result, we also prove the …

A hypergraph is Sperner if no hyperedge contains another one. A Sperner hypergraph is
equilizable (resp., threshold) if the characteristic vectors of its hyperedges are the (minimal) …

For a set L of positive integers, a set system\mathcal F ⊆ 2^ n F⊆ 2 n is said to be L-close
Sperner, if for any pair F, G of distinct sets in\mathcal FF the skew distance sd (F, G)=\min {| F …

A total dominating set in a graph is a subset of vertices such that every vertex in the graph
has a neighbor in it. A graph is said to be total domishold if it admits a total domishold …