Minimal non-FC-groups have been largely investigated and their structure is well-known. Minimal non-CC-groups, a first generalization of minimal non-FC-groups, have been investigated more recently and their complete description is still unknown. The present paper deals with generalizations of the notion of minimal non-FC-group in the context of locally nilpotent and locally solvable groups.

Neighborhood-perfect graphs form a subclass of the perfect graphs if the Strong Perfect Graph Conjecture of C. Berge is true. However, they are still not shown to be perfect. Here we propose the characterization of neighborhood-perfect graphs by studying minimal non-neighborhood-perfect graphs (MNNPG). After presenting some properties of MNNPGs, w e show that the only MNNPGs with neighborhood i...

We consider the most minimal scale invariant extension of the standard model that allows for successful radiative electroweak symmetry breaking and inflation. The framework involves an extra scalar singlet, that plays the rôle of the inflaton, and is compatibile with current experimental bounds owing to the non-minimal coupling of the latter to gravity. This inflationary scenario predicts a ver...

Seymour (Quart. J. Math. Oxford 25 (1974), 303-312) proved that a minimal non 2-colorable hypergraph on n vertices has at least n edges. A related fact is that a minimal unsatistiable CNF formula in n variables has at least n + 1 clauses (an unpublished result of M. Tarsi.) The link between the two results is shown; both are given infinite versions and proved using transversal theory (Seymour’s...

in this paper, a numerical method for nding minimal solution of a mn fullyfuzzy linear system of the form ax = b based on pseudo inverse calculation,is given when the central matrix of coecients is row full rank or column fullrank, and where a~ is a non-negative fuzzy mn matrix, the unknown vectorx is a vector consisting of n non-negative fuzzy numbers and the constant b isa vector consisti...