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Linear k-arboricity of Caylay Graphs on Abelian Groups with Given Degree

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Abstract

A linear k-forest is a forest whose components are paths of length at most k. The linear k-arboricity of a graph G, denoted by \(\mathrm{la}_k(G)\), is the least number of linear k-forests needed to decompose G. In this paper we study this invariant for Cayley graphs on Abelian groups with degree 3,4.

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Acknowledgements

We would like to thank the anonymous referees for a number of helpful comments and suggestions.

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Authors and Affiliations

  1. Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, International Research Center for Intelligent Perception and Computation, Xidian University, Xi’an, 710071, Shaanxi Province, China

    Nan Jia

  2. School of Mathematics and Statistics, Qinghai Normal University, Xining, 810008, Qinghai, China

    Yaping Mao

  3. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Zhao Wang

  4. Department of Mathematics and Statistics, Oakland University, Rochester, MI, 48309, USA

    Eddie Cheng

  5. Center for Mathematics and Interdisciplinary Sciences of Qinghai Province, Xining, 810008, Qinghai, China

    Yaping Mao & Eddie Cheng

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  1. Nan Jia
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  2. Yaping Mao
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  3. Zhao Wang
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  4. Eddie Cheng
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Correspondence to Yaping Mao.

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Supported by the National Science Foundation of China (Nos. 11601254, 11551001, 11161037, 11461054) and the Science Found of Qinghai Province (Nos. 2019-ZJ-921).

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Jia, N., Mao, Y., Wang, Z. et al. Linear k-arboricity of Caylay Graphs on Abelian Groups with Given Degree. Math.Comput.Sci. 15, 743–755 (2021). https://doi.org/10.1007/s11786-021-00503-6

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  • DOI: https://doi.org/10.1007/s11786-021-00503-6

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