The game chromatic index of some trees with maximum degree four and adjacent degree-four vertices
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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).
KeywordsGame 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.
- Andres SD (2003) Spieltheoretische Kantenfärbungsprobleme auf Wäldern und verwandte Strukturen (German), Diplomarbeit, Universität zu Köln (2003), 49–50; 55–56; 58; 61; 83–95; 97–123Google Scholar
- Bodlaender HL (1991) On the complexity of some colouring games. Graph-theoretic concepts in computer science (Berlin, 1990), 30–40, Lecture Notes in Comput. Sci., 484, Springer, Berlin, 1991Google Scholar