English

A conjecture on equitable vertex arboricity of graphs

Combinatorics 2012-11-22 v1 Discrete Mathematics

Abstract

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

Keywords

Cite

@article{arxiv.1211.4998,
  title  = {A conjecture on equitable vertex arboricity of graphs},
  author = {Xin Zhang and Jian-Liang Wu},
  journal= {arXiv preprint arXiv:1211.4998},
  year   = {2012}
}
R2 v1 2026-06-21T22:42:06.560Z