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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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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DOI: https://doi.org/10.1007/s00373-014-1466-5