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.2020.62
URN: urn:nbn:de:0030-drops-124694
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12469/
Guruswami, Venkatesan ;
Sandeep, Sai
d-To-1 Hardness of Coloring 3-Colorable Graphs with O(1) Colors
Abstract
The d-to-1 conjecture of Khot asserts that it is NP-hard to satisfy an ε fraction of constraints of a satisfiable d-to-1 Label Cover instance, for arbitrarily small ε > 0. We prove that the d-to-1 conjecture for any fixed d implies the hardness of coloring a 3-colorable graph with C colors for arbitrarily large integers C.
Earlier, the hardness of O(1)-coloring a 4-colorable graphs is known under the 2-to-1 conjecture, which is the strongest in the family of d-to-1 conjectures, and the hardness for 3-colorable graphs is known under a certain "fish-shaped" variant of the 2-to-1 conjecture.
BibTeX - Entry
@InProceedings{guruswami_et_al:LIPIcs:2020:12469,
author = {Venkatesan Guruswami and Sai Sandeep},
title = {{d-To-1 Hardness of Coloring 3-Colorable Graphs with O(1) Colors}},
booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
pages = {62:1--62:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-138-2},
ISSN = {1868-8969},
year = {2020},
volume = {168},
editor = {Artur Czumaj and Anuj Dawar and Emanuela Merelli},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12469},
URN = {urn:nbn:de:0030-drops-124694},
doi = {10.4230/LIPIcs.ICALP.2020.62},
annote = {Keywords: graph coloring, hardness of approximation}
}
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Keywords: |
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graph coloring, hardness of approximation |
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Collection: |
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47th International Colloquium on Automata, Languages, and Programming (ICALP 2020) |
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Issue Date: |
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2020 |
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Date of publication: |
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29.06.2020 |
