The main problem to be studied concerns cycle decompositions of complete graphs. The aim is to find the values of n for which complete graphs with n vertices have a decomposition into cycles of fixed odd length. Other problems related to cycle decompositons will be studied, such as the resolvability and nesting of cycle systems. Cycle decompositions constitute a special case of neighborhood designs which have found numerous applications in the design of statistical experiments, in particular of balanced incomplete block designs.
