# Edge arboricity : Do we need equitabilility ?

## TL;DR

This paper introduces equitable arboricity, a variant of graph arboricity requiring forests to have nearly equal edges, and proves it is equivalent to the traditional arboricity, allowing transformations without changing the number of forests.

## Contribution

The paper establishes the equivalence between equitable arboricity and traditional arboricity, providing a new perspective on graph decompositions.

## Key findings

- Equitable arboricity is equivalent to ordinary arboricity.
- Any arborescent decomposition can be transformed into an equitable one.
- Transformations do not alter the number of forests used.

## Abstract

In this paper we study a new variant of graph arboricity, which requires all the forests to have the same number of edges (up to a difference of 1). We prove that the new variant, which we call equitable arboricity, is equivalent to ordinary arboricity. In other words we show that any arborescent decomposition of a graph can be transformed into an equitable one without modifying the number of used forests.

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Source: https://tomesphere.com/paper/1705.00844