The game colouring number of powers of forests
We prove that the game colouring number of the $m$-th power of a forest of maximum degree $\Delta\ge3$ is bounded from above by \[\frac{(\Delta-1)^m-1}{\Delta-2}+2^m+1,\] which improves the best known bound by an asymptotic factor of 2.
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| Veröffentlicht in: | Discrete mathematics and theoretical computer science 2015-11, Vol.18 no. 1 (Graph Theory) |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We prove that the game colouring number of the $m$-th power of a forest of
maximum degree $\Delta\ge3$ is bounded from above by
\[\frac{(\Delta-1)^m-1}{\Delta-2}+2^m+1,\] which improves the best known bound
by an asymptotic factor of 2. |
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| ISSN: | 1365-8050 1365-8050 |
| DOI: | 10.46298/dmtcs.648 |