Equitable partition of graphs into induced linear forests

  • Xin ZhangEmail author
  • Bei Niu


It is proved that the vertex set of any simple graph G can be equitably partitioned into k subsets for any integer \(k\ge \max \{\big \lceil \frac{\Delta (G)+1}{2}\big \rceil ,\big \lceil \frac{|G|}{4}\big \rceil \}\) so that each of them induces a linear forest.


Equitable coloring Vertex arboricity Linear forest 



We are particularly grateful to Weichan Liu who suggests the constructive proofs of Lemmas 2.12.4, and also thanks Jingfen Lan, Bi Li, Yan Li and Qingsong Zou for their helpful discussions on shortening the proof of Theorem 1.3.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXidian UniversityXi’anChina

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