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arXiv · 1404.7259

Lower bounds for on-line graph colorings

Grzegorz Gutowski·Jakub Kozik·Piotr Micek·Xuding Zhu
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Abstract

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 $Ω(\frac{n}{\log n}^\frac{1}{3})$ colors. The best known on-line coloring algorithm for these graphs uses $O(n^{\frac{1}{2}})$ colors.

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Grzegorz Gutowski, Jakub Kozik, Piotr Micek, Xuding Zhu. 2015-10-09. Lower bounds for on-line graph colorings. https://doi.org/10.1007/978-3-319-13075-0_40

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