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arXiv · 2404.17011

First-Fit Coloring of Forests in Random Arrival Model

Bartłomiej Bosek·Grzegorz Gutowski·Michał Lasoń·Jakub Przybyło
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Abstract

We consider a graph coloring algorithm that processes vertices in order taken uniformly at random and assigns colors to them using First-Fit strategy. We show that this algorithm uses, in expectation, at most $(1 + o(1))\cdot \ln n \,/\, \ln\ln n$ different colors to color any forest with $n$ vertices. We also construct a family of forests that shows that this bound is best possible.

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Bartłomiej Bosek, Grzegorz Gutowski, Michał Lasoń, Jakub Przybyło. 2024-04-25. First-Fit Coloring of Forests in Random Arrival Model. https://doi.org/10.4230/lipics.mfcs.2024.33

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