Molecular approaches were used to re-evaluate the morphological criteria used to identify plant-associated Verticillium species. ITS-RFLPs divided the 31 studied strains of seven Verticillium species, (including the type species V. luteo-album) into four clusters. Cluster one comprised strains of the type species, V. luteo-album, cluster two V. albo-atrum, V. dahliae, V. nubilum and V. tricorpu...

A 3-way \((v,k,t)\) trade \(T\) of volume \(m\) consists three pairwise disjoint collections \(T_{1}\), \(T_{2}\) and \(T_{3}\), each blocks size \(k\), such that for every \(t\)-subset \(v\)-set \(V\), the number containing this is same in \(T_{i}\) \(1\leq i\leq 3\). If any found(\(T\)) occurs at most once 3\), then called Steiner trade. We attempt to complete spectrum \(S_{3s}(v,k)\), set al...