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arXiv · 1910.02063

Fully Dynamic $(\Delta+1)$-Coloring in Constant Update Time

Sayan Bhattacharya·Fabrizio Grandoni·Janardhan Kulkarni·Quanquan C. Liu·Shay Solomon
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Abstract

The problem of (vertex) $(\Delta+1)$-coloring a graph of maximum degree $\Delta$ has been extremely well-studied over the years in various settings and models. Surprisingly, for the dynamic setting, almost nothing was known until recently. In SODA'18, Bhattacharya, Chakrabarty, Henzinger and Nanongkai devised a randomized data structure for maintaining a $(\Delta+1)$-coloring with $O(\log \Delta)$ expected amortized update time. In this paper, we present a $(\Delta+1)$-coloring data structure that achieves a constant amortized update time and show that this time bound holds not only in expectation but also with high probability.

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Sayan Bhattacharya, Fabrizio Grandoni, Janardhan Kulkarni, Quanquan C. Liu, Shay Solomon. 2019-10-04. Fully Dynamic $(\Delta+1)$-Coloring in Constant Update Time. https://arxiv.org/abs/1910.02063

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