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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
Article
  • 123 Downloads

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).

Keywords

Game chromatic index Tree Graph coloring game Game chromatic number 

Notes

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.

References

  1. 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
  2. Andres SD (2006) The game chromatic index of forests of maximum degree \(\Delta \ge 5\). Discrete Appl Math 154(9):1317–1323MathSciNetCrossRefzbMATHGoogle Scholar
  3. 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
  4. Cai L, Zhu X (2001) Game chromatic index of k-degenerate graphs. J. Graph Theory 36:144–155MathSciNetCrossRefzbMATHGoogle Scholar
  5. Chan WH, Nong G (2014) The game chromatic index of some trees of maximum degree 4. Discrete Appl Math 170:1–6MathSciNetCrossRefzbMATHGoogle Scholar
  6. Erdös P, Faigle U, Hochstättler W, Kern W (2004) Note on the game chromatic index of trees. Theor Comput Sci 313:371–376MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

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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