Kirkman school project designs Original Research Article

A Kirkman school project design on v elements consists of the maximum admissible number of disjoint parallel classes, each containing blocks of sizes three except possibly one of size two or four. Černý, Horák, and Wallis completely settled existence when v≡0,2 (mod 3) and made some progress and advanced a conjecture when v≡1 (mod 3). In this paper, a complete solution for the existence of such designs when v≡4 (mod 6) is given, and a nearly complete solution when v≡1 (mod 6) is also given.