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Pseudorandom Sets in Grassmann Graph Have Near-Perfect Expansion | IEEE Conference Publication | IEEE Xplore

Pseudorandom Sets in Grassmann Graph Have Near-Perfect Expansion


Abstract:

We prove that pseudorandom sets in the Grassmann graph have near-perfect expansion. This completes the last missing piece of the proof of the 2-to-2-Games Conjecture (alb...Show More

Abstract:

We prove that pseudorandom sets in the Grassmann graph have near-perfect expansion. This completes the last missing piece of the proof of the 2-to-2-Games Conjecture (albeit with imperfect completeness). The Grassmann graph has induced subgraphs that are themselves isomorphic to Grassmann graphs of lower orders. A set of vertices is called pseudorandom if its density within all such subgraphs (of constant order) is at most slightly higher than its density in the entire graph. We prove that pseudorandom sets have almost no edges within them. Namely, their edge-expansion is very close to 1.
Date of Conference: 07-09 October 2018
Date Added to IEEE Xplore: 02 December 2018
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Conference Location: Paris, France

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