eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-07-02
89:1
89:9
10.4230/LIPIcs.ICALP.2021.89
article
Improving Gebauer’s Construction of 3-Chromatic Hypergraphs with Few Edges
Kozik, Jakub
1
https://orcid.org/0000-0002-1362-7780
Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
In 1964 Erdős proved, by randomized construction, that the minimum number of edges in a k-graph that is not two colorable is O(k² 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 a derandomization technique we reduce that number to 2^{k+Θ̃(k^{1/2})}.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol198-icalp2021/LIPIcs.ICALP.2021.89/LIPIcs.ICALP.2021.89.pdf
Property B
Hypergraph Coloring
Deterministic Constructions