Spanning cubic graph designs

Graph designs are natural extensions of BIBDs (balanced incomplete block designs). In this paper we explore spanning cubic graph designs and develop tools for constructing some of them. We show that K16K16 can be decomposed into each of the 4060 connected cubic graphs of order 16, and into precisely 144 of the 147 disconnected cubic graphs of order 16. We also identify some infinite families of cubic graphs of order 6n+46n+4 that decompose K6n+4K6n+4.