Randomly coloring simple hypergraphs

We study the problem of constructing a (near) uniform random proper q-coloring of a simple k-uniform hypergraph with n vertices and maximum degree Δ. (Proper in that no edge is mono-colored and simple in that two edges have maximum intersection of size one.) We show that if for some α<1 we have Δ?nα and q?Δ(1+α)/kα then Glauber dynamics will become close to uniform in time from a random (improper) start. Note that for k>1+α−1 we can take q=o(Δ).