A Weaker Version of a Conjecture on List Vertex Arboricity of Graphs (original) (raw)

Abstract

The vertex arboricity \(\rho (G)\) of a graph \(G\) is the minimum number of colors to color \(G\) such that each color class induces a forest. The list vertex arboricity \(\rho _l(G)\) is the list-coloring version of this concept. Zhen and Wu conjectured that \(\rho _l(G)=\rho (G)\) whenever \(|V(G)|\le 3\rho (G)\). In this paper, we prove the weaker version of the conjecture obtained by replacing \(3\rho (G)\) with \(\frac{5}{2}\rho (G)+\frac{1}{2}\).

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Acknowledgments

The authors are grateful to the referees for their careful reading and valuable comments. This work is supported by NSFC (11161046), Xinjiang Young Talent Project (2013721012).

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Authors and Affiliations

  1. College of Information Engineering, Tarim University, Alar, 843300, People’s Republic of China
    Wei Wang, Zhidan Yan & Nini Xue
  2. College of Mathematics and System Science, Xinjiang University, Urumqi, 830046, People’s Republic of China
    Baoyindureng Wu

Authors

  1. Wei Wang
  2. Baoyindureng Wu
  3. Zhidan Yan
  4. Nini Xue

Corresponding author

Correspondence toBaoyindureng Wu.

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Wang, W., Wu, B., Yan, Z. et al. A Weaker Version of a Conjecture on List Vertex Arboricity of Graphs.Graphs and Combinatorics 31, 1779–1787 (2015). https://doi.org/10.1007/s00373-014-1466-5

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