Kirkman school project designs (Q1301652)

A Kirkman school project (KSP) design on \(v\) elements consists of the maximum admissible number of disjoint parallel classes each containing blocks of size three except possibly one of size two or four. The existence problem for KSP designs with \(v \equiv 0,2\) (mod 3) was settled by \textit{A. Černý, P. Horák} and \textit{W. D. Wallis} [Discrete Math. 167/168, 189-196 (1997; Zbl 0873.05015)]. In the paper under review, the authors completely resolve the existence problem for \(v \equiv 4\) (mod 3) and nearly completely cover the case \(v \equiv 1\) (mod 3).