ON SENSITIVITY OF k-UNIFORM HYPERGRAPH PROPERTIES

In this paper we present a graph property with sensitivity Θ( √ n), where n = (v 2 ) is the number of variables, and generalize it to a k-uniform hypergraph property with sensitivity Θ( √ n), where n = (v k ) is again the number of variables. This yields the smallest sensitivity yet achieved for a k-uniform hypergraph property. We then show that, for even k, there is a k-uniform hypergraph property that demonstrates a quadratic gap between sensitivity and block sensitivity. This matches the previously known largest gap found by Rubinstein (1995) for a general Boolean function and Chakraborty (2005) for a cyclically invariant Boolean function, and is the first known example of such a gap for a graph or hypergraph property.