eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-29
62:1
62:12
10.4230/LIPIcs.ICALP.2020.62
article
d-To-1 Hardness of Coloring 3-Colorable Graphs with O(1) Colors
Guruswami, Venkatesan
1
Sandeep, Sai
1
Carnegie Mellon University, Pittsburgh, PA, USA
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol168-icalp2020/LIPIcs.ICALP.2020.62/LIPIcs.ICALP.2020.62.pdf
graph coloring
hardness of approximation