Kneser graphs are like Swiss cheese

Ehud Friedgut, Oded Regev
2018 Discrete Analysis  
We prove that for a large family of product graphs, and for Kneser graphs K(n, αn) with fixed α < 1/2, the following holds. Any set of vertices that spans a small proportion of the edges in the graph can be made independent by removing a small proportion of the vertices of the graph. This allows us to strengthen the results of [3] and [2], and show that any independent set in these graphs is almost contained in an independent set which depends on few coordinates. Our proof is inspired by, and
more » ... inspired by, and follows some of the main ideas of, Fox's proof of the graph removal lemma [6] .
doi:10.19086/da.3103 fatcat:otcjyje3yfguvf7rzvzs32gx3i