Improved bounds for coloring locally sparse hypergraphs

April 05, 2020 · The Ethereal · 🏛 International Workshop and International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques

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Authors Fotis Iliopoulos arXiv ID 2004.02066 Category cs.DM: Discrete Mathematics Cross-listed cs.DS, math.CO Citations 3 Venue International Workshop and International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques Last Checked 2 months ago
Abstract
We show that, for every $k \ge 2$, every $k$-uniform hypergaph of degree $Δ$ and girth at least $5$ is efficiently $(1+o(1) )(k-1) (Δ/ \ln Δ)^{ 1/(k-1) } $-list colorable. As an application (and to the best of our knowledge) we obtain the currently best algorithm for list-coloring random hypergraphs of bounded average degree.
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