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Equitable partition of graphs into induced linear forests

Combinatorics 2019-08-15 v1 Discrete Mathematics

Abstract

It is proved that the vertex set of any simple graph GG can be equitably partitioned into kk subsets for any integer kmax{Δ(G)+12,G4}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.

Keywords

Cite

@article{arxiv.1908.05075,
  title  = {Equitable partition of graphs into induced linear forests},
  author = {Xin Zhang and Bei Niu},
  journal= {arXiv preprint arXiv:1908.05075},
  year   = {2019}
}
R2 v1 2026-06-23T10:47:18.637Z