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arXiv · 1502.04963

Exact bounds for distributed graph colouring

Joel Rybicki·Jukka Suomela
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Abstract

We prove exact bounds on the time complexity of distributed graph colouring. If we are given a directed path that is properly coloured with $n$ colours, by prior work it is known that we can find a proper 3-colouring in $\frac{1}{2} \log^*(n) \pm O(1)$ communication rounds. We close the gap between upper and lower bounds: we show that for infinitely many $n$ the time complexity is precisely $\frac{1}{2} \log^* n$ communication rounds.

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Joel Rybicki, Jukka Suomela. 2015-02-17. Exact bounds for distributed graph colouring. https://arxiv.org/abs/1502.04963

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