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Equitable vertex arboricity of 5-degenerate graphs

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Abstract

Wu et al. (Discret Math 313:2696–2701, 2013) conjectured that the vertex set of any simple graph G can be equitably partitioned into m subsets so that each subset induces a forest, where \(\Delta (G)\) is the maximum degree of G and m is an integer with \(m\ge \lceil \frac{\Delta (G)+1}{2}\rceil \). This conjecture is verified for 5-degenerate graphs in this paper.

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Acknowledgments

This work was in part supported by National Science Foundation of China (11271006, 11471193), National Youth Foundation of China (11401386, 11501316), Shandong Provincial Natural Science Foundation of China (ZR2014AQ001), Independent Innovation Foundation of Shandong University (IFYT 14013) and China Scholarship Council (No. 201406220192).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Georgia State University, Atlanta, GA, 30303, USA

    Guantao Chen

  2. School of Mathematics, Shandong University, Jinan, 250100, China

    Yuping Gao, Guanghui Wang & Jianliang Wu

  3. Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA

    Songling Shan

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  1. Guantao Chen
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  2. Yuping Gao
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  3. Songling Shan
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  4. Guanghui Wang
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  5. Jianliang Wu
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Correspondence to Jianliang Wu.

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Chen, G., Gao, Y., Shan, S. et al. Equitable vertex arboricity of 5-degenerate graphs. J Comb Optim 34, 426–432 (2017). https://doi.org/10.1007/s10878-016-9997-8

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  • DOI: https://doi.org/10.1007/s10878-016-9997-8

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