Abstract:
A pedigree of a population of individuals is a finite directed acyclic graph in which each vertex has indegree 0 or 2. The sink vertices in a pedigree are living individuals and sources are the founders of a population. I will define the problem of reconstructing a pedigree from its proper sub-pedigrees (pedigrees of proper subsets of the living population). I will then sketch a construction of non-reconstructible pedigrees. The problem of characterising such examples has nice connections with line graphs, permutation groups, and the results of Lovász and Nash-Williams on some classical reconstruction problems. This is work in progress.