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Haplotyping is the process of reconstructing the genetic information donated by a prior generation to form a current population. Haplotyping is important because it allows us to study how traits are passed from one generation to another, which in turn allows us to find genetic markers that describe a current population's susceptibility to diseases. Our goal is to study the underlying graph theory problem, and we study the bipartite graphs, called diversity graphs, that describe haplotyping. In particular, we investigate the problem of finding the minimum number of haplotypes that can reconstruct a population, called the Pure Parsimony problem. The graph theory representation provides significant insight if the number of mates is restricted.

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