Unique Least Common Ancestors and Clusters in Directed Acyclic Graphs
Discrete Mathematics
2023-09-26 v1 Combinatorics
Populations and Evolution
Abstract
We investigate the connections between clusters and least common ancestors (LCAs) in directed acyclic graphs (DAGs). We focus on the class of DAGs having unique least common ancestors for certain subsets of their minimal elements since these are of interest, particularly as models of phylogenetic networks. Here, we use the close connection between the canonical k-ary transit function and the closure function on a set system to show that pre-k-ary clustering systems are exactly those that derive from a class of DAGs with unique LCAs. Moreover, we show that k-ary T-systems and k-weak hierarchies are associated with DAGs that satisfy stronger conditions on the existence of unique LCAs for sets of size at most k.
Cite
@article{arxiv.2309.13634,
title = {Unique Least Common Ancestors and Clusters in Directed Acyclic Graphs},
author = {Ameera Vaheeda Shanavas and Manoj Changat and Marc Hellmuth and Peter F. Stadler},
journal= {arXiv preprint arXiv:2309.13634},
year = {2023}
}