Before revision:  Our results generalize previous results for accessibility percolation on the biallelic hypercube, and compare favorably to published numerical results for multiallelic Hamming graphs . A key tool of our analysis is the concept of quasi-accessibility, which eliminates the need to account for the self-avoidance of accessible paths .
After revision:  Our results generalize previous results for accessibility percolation on the biallelic hypercube, and compare favorably to published numerical results for multiallelic Hamming graphs .