Lower bounds for sensitivity of graph properties

TL;DR

This paper establishes a lower bound on the sensitivity of any non-trivial graph property, showing it must be at least half the number of vertices for large graphs.

Contribution

It provides a new theoretical lower bound on the sensitivity of graph properties, advancing understanding in graph property complexity.

Findings

Sensitivity of non-trivial graph properties is at least half the number of vertices.

The bound holds for sufficiently large graphs.

This result improves previous bounds in the field.

Abstract

We prove that the sensitivity of any non-trivial graph property on $n$ vertices is at least $\lfloor \frac{1}{2}n \rfloor$ , provided $n$ is sufficiently large.