Journal of Combinatorial Optimization

, Volume 36, Issue 1, pp 1–12 | Cite as

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

  • Wai Lam Fong
  • Wai Hong Chan
  • Ge Nong


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).


Game chromatic index Tree Graph coloring game Game chromatic number 



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. 1.Department of Mathematics and Information TechnologyThe Education University of Hong KongTai PoChina
  2. 2.Department of Computer ScienceSun Yat-sen UniversityGuangzhouChina
  3. 3.SYSU-CMU Shunde International Joint Research InstituteGuangzhouChina

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