Combinatorics of Pedigrees I: Counterexamples to a Reconstruction Question

@article{Thatte2008CombinatoricsOP,
title={Combinatorics of Pedigrees I: Counterexamples to a Reconstruction Question},
author={Bhalchandra D. Thatte},
journal={SIAM J. Discrete Math.},
year={2008},
volume={22},
pages={961-970}
}

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… CONTINUE READING