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DOI: 10.4230/LIPIcs.ICALP.2018.46
URN: urn:nbn:de:0030-drops-90505
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9050/
Duraj, Lech ; Gutowski, Grzegorz ; Kozik, Jakub
A Note on Two-Colorability of Nonuniform Hypergraphs
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Abstract
For a hypergraph H, let q(H) denote the expected number of monochromatic edges when the color of each vertex in H is sampled uniformly at random from the set of size 2. Let s_{min}(H) denote the minimum size of an edge in H. Erdös asked in 1963 whether there exists an unbounded function g(k) such that any hypergraph H with s_{min}(H) >=slant k and q(H) <=slant g(k) is two colorable. Beck in 1978 answered this question in the affirmative for a function g(k) = Theta(log^* k). We improve this result by showing that, for an absolute constant delta>0, a version of random greedy coloring procedure is likely to find a proper two coloring for any hypergraph H with s_{min}(H) >=slant k and q(H) <=slant delta * log k.
BibTeX - Entry
@InProceedings{duraj_et_al:LIPIcs:2018:9050,
author = {Lech Duraj and Grzegorz Gutowski and Jakub Kozik},
title = {{A Note on Two-Colorability of Nonuniform Hypergraphs}},
booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
pages = {46:1--46:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-076-7},
ISSN = {1868-8969},
year = {2018},
volume = {107},
editor = {Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9050},
URN = {urn:nbn:de:0030-drops-90505},
doi = {10.4230/LIPIcs.ICALP.2018.46},
annote = {Keywords: Property B, Nonuniform Hypergraphs, Hypergraph Coloring, Random Greedy Coloring}
}
| Keywords: | Property B, Nonuniform Hypergraphs, Hypergraph Coloring, Random Greedy Coloring | |
| Seminar: | 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 04.07.2018 |
