License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2018.15
URN: urn:nbn:de:0030-drops-90190
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9019/
Bhangale, Amey
NP-Hardness of Coloring 2-Colorable Hypergraph with Poly-Logarithmically Many Colors
Abstract
We give very short and simple proofs of the following statements: Given a 2-colorable 4-uniform hypergraph on n vertices,
1) It is NP-hard to color it with log^delta n colors for some delta>0.
2) It is quasi-NP-hard to color it with O({log^{1-o(1)} n}) colors.
In terms of NP-hardness, it improves the result of Guruswam, HÃ¥stad and Sudani [SIAM Journal on Computing, 2002], combined with Moshkovitz-Raz [Journal of the ACM, 2010], by an `exponential' factor. The second result improves the result of Saket [Conference on Computational Complexity (CCC), 2014] which shows quasi-NP-hardness of coloring a 2-colorable 4-uniform hypergraph with O(log^gamma n) colors for a sufficiently small constant 1 >> gamma>0.
Our result is the first to show the NP-hardness of coloring a c-colorable k-uniform hypergraph with poly-logarithmically many colors, for any constants c >= 2 and k >= 3.
BibTeX - Entry
@InProceedings{bhangale:LIPIcs:2018:9019,
author = {Amey Bhangale},
title = {{NP-Hardness of Coloring 2-Colorable Hypergraph with Poly-Logarithmically Many Colors}},
booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
pages = {15:1--15:11},
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/2018/9019},
URN = {urn:nbn:de:0030-drops-90190},
doi = {10.4230/LIPIcs.ICALP.2018.15},
annote = {Keywords: Hypergraph coloring, Inapproximability, Schrijver graph}
}
Keywords: |
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Hypergraph coloring, Inapproximability, Schrijver graph |
Collection: |
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45th International Colloquium on Automata, Languages, and Programming (ICALP 2018) |
Issue Date: |
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2018 |
Date of publication: |
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04.07.2018 |