Improving Gebauer's construction of 3-chromatic hypergraphs with few edges

02/23/2021

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by   Jakub Kozik, et al.

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In 1964 Erdős proved, by randomized construction, that the minimum number of edges in a k-graph that is not two colorable is O(k^2 2^k). To this day, it is not known whether there exist such k-graphs with smaller number of edges. Known deterministic constructions use much larger number of edges. The most recent one by Gebauer requires 2^k+Θ(k^2/3) edges. Applying derandomization technique we reduce that number to 2^k+Θ(k^1/2).