Minimum communication cost for zero knowledge proofs of three colorability
So here is the right paper for my purposes:

Joe Kilian, "A note on efficient zero-knowledge proofs and arguments." http://people.csail.mit.edu/vinodv/6892-Fall2013/efficientargs.pdf

To get the strongest result, we need to accept zero knowledge arguments rather than proofs (computationally bounded prover); these are what I am interested in but did not know the terminology.

Assuming sufficient cryptographic assumptions, the paper gives zero knowledge arguments with total communication $O(b \log^c n \log (1/p))$ for $c = O(1)$.

This result is tightened to $O(1)$ rounds by Ishai et al., "On Efficient Zero-Knowledge PCPs", http://www.cs.virginia.edu/~mohammad/files/papers/13%20ZKPCPs.pdf.