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.

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.