How to see the forest for the trees
Discrete Mathematics
2025-10-29 v1 Combinatorics
Abstract
One of the major starting points of discrete optimization is the theorem of Nash-Williams and Tutte on the existence of disjoint spanning trees of a graph along with its counterpart on the existence of forests covering all edges of the graph. These elegant results triggered a comprehensive research that gave rise to far-reaching generalizations and found applications at seemingly far-fetched areas. There are well over a thousand papers in the literature, including quite a few brand-new ones. Our first goal is to enlighten some aspects and links of these developments with the hope that the melody finds its way to non-experts. But we hope that experts will also find some novelties in our orchestration.
Keywords
Cite
@article{arxiv.2510.23614,
title = {How to see the forest for the trees},
author = {Erika Bérczi-Kovács and András Frank},
journal= {arXiv preprint arXiv:2510.23614},
year = {2025}
}