We consider the problem of decomposing a complete graph into the Cartesian product of two complete graphs Kr and Kc. This problem originated from the clone library screening. We give a general method of constructing such decompositions using various sorts of combinatorial designs. In particular, for r=3 and c=3, we show that such a decomposition exists for all n satisfying some simple necessary conditions.
- Graph decomposition and grid-blocks
- Grid-block designs