Hardness of finding independent sets in almost q-colorable graphs

Subhash Khot, Rishi Saket

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We show that for any ε > 0, and positive integers k and q such that q ≥= 2k + 1, given a graph on N vertices that has a q-colorable induced sub graph of (1 - ε)N vertices, it is NP-hard to find an independent set of N/qk+1 vertices. This substantially improves upon the work of Dinur et al. [DKPS] who gave a corresponding bound of N/q2. Our result implies that for any positive integer k, given a graph that has an independent set of ≈ (2k + 1)-1 fraction of vertices, it is NP-hard to find an independent set of (2k + 1)-(k+1) fraction of vertices. This improves on the previous work of Engebretsen and Holmerin [EH] who proved a gap of ≈ 2-k vs 2-(k 2), which is best possible using techniques (including those of [EH]) based on the query efficient PCP of Samorodnitsky and Trevisan [3].

Original languageEnglish (US)
Title of host publicationProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Pages380-389
Number of pages10
DOIs
StatePublished - 2012
Event53rd Annual IEEE Symposium on Foundations of Computer Science, FOCS 2012 - New Brunswick, NJ, United States
Duration: Oct 20 2012Oct 23 2012

Other

Other53rd Annual IEEE Symposium on Foundations of Computer Science, FOCS 2012
CountryUnited States
CityNew Brunswick, NJ
Period10/20/1210/23/12

Keywords

  • Coloring
  • Graphs
  • Hardness
  • Independent-Set
  • PCP

ASJC Scopus subject areas

  • Computer Science(all)

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