Lower Bounds for On-line Graph Colorings

@inproceedings{Gutowski2014LowerBF,
  title={Lower Bounds for On-line Graph Colorings},
  author={G. Gutowski and J. Kozik and Piotr Micek and Xuding Zhu},
  booktitle={ISAAC},
  year={2014}
}
We propose two strategies for Presenter in on-line graph coloring games. The first one constructs bipartite graphs and forces any on-line coloring algorithm to use \(2\log _2 n - 10\) colors, where \(n\) is the number of vertices in the constructed graph. This is best possible up to an additive constant. The second strategy constructs graphs that contain neither \(C_3\) nor \(C_5\) as a subgraph and forces \(\varOmega (\frac{n}{\log n}^\frac{1}{3})\) colors. The best known on-line coloring… Expand
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