In this article I derive an alternative algorithm to Hudson and Kaplan's (Genetics 111, 147-165) algorithm that gives a lower bound to the number of recombination events in a sample's history. It is shown that the number, T _M, found by the algorithm is the least number of topologies required to explain a set of DNA sequences sampled under the infinite-site assumption. Let T=(T₁,⋯,T_r) be a list of topologies compatible with the sequences, i.e., T_k is compatible with an interval, I _k, of sites in the alignment. A characterization of all lists having T_M topologies is given and it is shown that T_M relates to specific patterns in the alignment, here called chain series. Further, a number of theorems relating general lists of topologies to the number T_M is presented. The results are discussed in relation to the true minimum number of recombination events required to explain an alignment.