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The game chromatic index of some trees with maximum degree four and adjacent degree-four vertices

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Abstract

We prove that the game chromatic index of trees of maximum degree 4 with every 4-vertex (degree-four vertex) being adjacent to at most one 4-vertex does not exceed 5. This relaxes the assumption that the trees do not contain adjacent 4-vertices in the result of Chan and Nong (Discrete Appl Math 170:1–6, 2014).

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Acknowledgements

W.H. Chan was partially supported by the General Research Fund (18300215) from the Research Grant Council of the University Grants Committee of Hong Kong SAR. G. Nong was supported by the Guangzhou Science and Technology Program Grant 201707010165 and the Guangdong Science and Technology Program Grant 2017A050506025.

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Authors and Affiliations

  1. Department of Mathematics and Information Technology, The Education University of Hong Kong, Tai Po, Hong Kong SAR, China

    Wai Lam Fong & Wai Hong Chan

  2. Department of Computer Science, Sun Yat-sen University, Guangzhou, China

    Ge Nong

  3. SYSU-CMU Shunde International Joint Research Institute, Guangzhou, China

    Ge Nong

Authors
  1. Wai Lam Fong
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  2. Wai Hong Chan
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  3. Ge Nong
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Correspondence to Wai Hong Chan.

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Fong, W.L., Chan, W.H. & Nong, G. The game chromatic index of some trees with maximum degree four and adjacent degree-four vertices. J Comb Optim 36, 1–12 (2018). https://doi.org/10.1007/s10878-018-0277-7

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  • DOI: https://doi.org/10.1007/s10878-018-0277-7

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