A conjecture on equitable vertex arboricity of graphs

TL;DR

This paper proves a conjecture that any simple graph with maximum degree at least half its vertices can be equitably partitioned into subsets inducing forests, advancing understanding of graph arboricity.

Contribution

The paper confirms Wu, Zhang, and Li's conjecture for graphs with maximum degree at least half the number of vertices.

Findings

Conjecture holds for graphs with Δ(G) ≥ |G|/2

Provides a proof for a specific class of graphs

Advances the theory of equitable vertex arboricity

Abstract

Wu, Zhang and Li [4] conjectured that the set of vertices of any simple graph $G$ can be equitably partitioned into $\lceil(\Delta(G)+1)/2\rceil$ subsets so that each of them induces a forest of $G$. In this note, we prove this conjecture for graphs $G$ with $\Delta(G)\geq |G|/2$.