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URN: urn:nbn:de:0030-drops-124694
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d-To-1 Hardness of Coloring 3-Colorable Graphs with O(1) Colors

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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}
}

Keywords: graph coloring, hardness of approximation
Seminar: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue date: 2020
Date of publication: 29.06.2020


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