On Independent Sets, 2-to-2 Games and Grassmann Graphs

  title={On Independent Sets, 2-to-2 Games and Grassmann Graphs},
  author={Subhash Khot and Dor Minzer and Shmuel Safra},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
We present a candidate reduction from the 3-Lin problem to the 2-to-2 Games problem and present a combinatorial hypothesis about Grassmann graphs which, if correct, is sufficient to show the soundness of the reduction in a certain non-standard sense. A reduction that is sound in this non-standard sense implies that it is NP-hard to distinguish whether an <i>n</i>-vertex graph has an independent set of size ( 1− 1/√2 ) <i>n</i> − <i>o</i>(<i>n</i>) or whether every independent set has size… CONTINUE READING
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