Results in Configuration Ordering

In this chapter, we look at configuration orderings for block designs. We discuss standard configuration ordering, a listing of the blocks of a design such that sets of consecutive blocks are isomorphic to a given configuration. We present all the known results within the configuration ordering framework. The majority of results in this area arise from considering the Hamiltonicity of the block-intersection graph. Configuration orderings imply the existence of configuration decompositions. We then turn to generalized configuration orderings where a set of allowable configurations is permitted and similarly review all known results. We conclude the chapter with a look at configuration orderings for graph decompositions other than those represented by balanced incomplete block designs and pairwise balanced designs. This chapter will be of particular interest to the researcher interested in seeing all known results collected within a unified framework. This chapter will also be of interest to the researcher wanting to see the relatively recent work in generalized configuration ordering. Finally, this chapter will be of interest to the researcher wanting to see orderings for designs other than balanced incomplete block designs and pairwise balanced designs.