  We prove an upper bound for the $\varepsilon$-mixing time of the symmetric
exclusion process on any graph G, with any feasible number of particles. Our
estimate is proportional to $\mathsf{T}_{\mathsf{RW}(G)}\ln(|V|/\varepsilon)$,
where |V| is the number of vertices in G, and $\mathsf{T}_{\mathsf{RW}(G)}$ is
the 1/4-mixing time of the corresponding single-particle random walk. This
bound implies new results for symmetric exclusion on expanders, percolation
clusters, the giant component of the Erdos-Renyi random graph and Poisson point
processes in $\mathbb{R}^d$. Our technical tools include a variant of Morris's
chameleon process.
