License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2021.89
URN: urn:nbn:de:0030-drops-141587
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14158/
Kozik, Jakub
Improving Gebauer’s Construction of 3-Chromatic Hypergraphs with Few Edges
Abstract
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})}.
BibTeX - Entry
@InProceedings{kozik:LIPIcs.ICALP.2021.89,
author = {Kozik, Jakub},
title = {{Improving Gebauer’s Construction of 3-Chromatic Hypergraphs with Few Edges}},
booktitle = {48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
pages = {89:1--89:9},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-195-5},
ISSN = {1868-8969},
year = {2021},
volume = {198},
editor = {Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/14158},
URN = {urn:nbn:de:0030-drops-141587},
doi = {10.4230/LIPIcs.ICALP.2021.89},
annote = {Keywords: Property B, Hypergraph Coloring, Deterministic Constructions}
}
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Keywords: |
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Property B, Hypergraph Coloring, Deterministic Constructions |
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Collection: |
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48th International Colloquium on Automata, Languages, and Programming (ICALP 2021) |
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Issue Date: |
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2021 |
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Date of publication: |
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02.07.2021 |
