# Equitable partition of graphs into induced linear forests

## TL;DR

This paper proves that any simple graph can be equitably partitioned into a specified number of subsets, each inducing a linear forest, under certain conditions related to maximum degree and size.

## Contribution

It establishes a new equitable partition theorem for graphs into induced linear forests based on degree and size constraints.

## Key findings

- Partition exists for k ≥ max{ceil((Δ(G)+1)/2), ceil(|G|/4)}
- Each subset induces a linear forest
- Applicable to all simple graphs

## Abstract

It is proved that the vertex set of any simple graph $G$ can be equitably partitioned into $k$ subsets for any integer $k\geq\max\{\big\lceil\frac{\Delta(G)+1}{2}\big\rceil,\big\lceil\frac{|G|}{4}\big\rceil\}$ so that each of them induces a linear forest.