When a forest, narrowed to an atom of subset algebra, turns out to be a tree
Combinatorics
2025-02-18 v3
Abstract
It is proved that the restriction of a and -component directed spanning forest of minimal weight to an atom of the subset algebra generated by the sets of vertices of trees of -component minimal spanning forests is a tree. For spanning minimal forests consisting of fewer components, this property, generally speaking, does not exist.
Cite
@article{arxiv.2501.19068,
title = {When a forest, narrowed to an atom of subset algebra, turns out to be a tree},
author = {Vasily Buslov},
journal= {arXiv preprint arXiv:2501.19068},
year = {2025}
}
Comments
Significant inaccuracies in the English translation