# Decomposing graphs into forests

## TL;DR

This paper presents a straightforward graph-theoretic proof of Nash-Williams' theorem on covering graphs with forests, including a generalization allowing preassigned edges to specific forests, enhancing understanding of graph decompositions.

## Contribution

The paper offers a simple proof of Nash-Williams' classical result and extends it to cases with preassigned edges, broadening its applicability.

## Key findings

- Provided a simple proof of Nash-Williams' theorem
- Extended the theorem to include preassigned edges
- Enhanced understanding of graph decompositions into forests

## Abstract

We give a simple graph-theoretic proof of a classical result due to C. St. J. A. Nash-Williams on covering graphs by forests. Moreover we derive a slight generalisation of this statement where some edges are preassigned to distinct forests.