  A pedigree is a directed graph in which each vertex (except the founder
vertices) has two parents. The main result in this paper is a construction of
an infinite family of counter examples to a reconstruction problem on
pedigrees, thus negatively answering a question of Steel and Hein. Some
positive reconstruction results are also presented. The problem of counting
distinct (mutually non-isomorphic) pedigrees is considered. The known lower and
upper bounds on the number of pedigrees are improved upon, and their relevance
to pedigree reconstruction from DNA sequence data is discussed. It is shown
that the information theoretic bound on the number of segregating sites in the
sequence data that is minimally essential for reconstructing pedigrees would
not significantly change with improved enumerative estimates.
