On Separating Families of Bipartitions
Combinatorics
2011-11-08 v1
Abstract
In this paper, we focus on families of bipartitions, i.e. set partitions consisting of at most two components. We say that a family of bipartitions is a separating family for a set if every two elements in can be separated by some bipartition. Furthermore, we call a separating family minimal if no proper subfamily is a separating family. We characterize the set of all minimal separating families of maximum size for arbitrary set as the set of all spanning trees on and enumerate minimal separating families of maximum size. Furthermore, we enumerate separating families of arbitrary size, which need not be minimal.
Keywords
Cite
@article{arxiv.1111.1376,
title = {On Separating Families of Bipartitions},
author = {Takahisa Toda and Ivo Vigan},
journal= {arXiv preprint arXiv:1111.1376},
year = {2011}
}