This paper deals with the question of completing a monotone increasing family of subsets Gamma of a finite set Omega to obtain the linearly dependent subsets of a family of vectors of a vector space. Specifically, we prove ...

A dominating set of a graph is a vertex subset such that every vertexnot in the subset is adjacent to at least one in the subset. In this paper westudy whenever there exists a new dominating set contained (respectively, ...