We consider a random fitness landscape on the space of haploid diallelic genotypes
with n genetic loci, where each genotype is considered either inviable or viable depending
on whether or not there are any incompatibilities among its allele pairs. We suppose that
each allele pair in the set of all possible allele pairs on the n loci is independently
incompatible with probability p=c/(2n). We examine the connectivity of the viable genotypes
under single locus mutations and show that, for 01, there are no viable genotypes with probability
converging to one. The genotype space is equivalent to the n-dimensional hypercube and the
viable genotypes are solutions to a random 2-SAT problem, so the same result holds for the
connectivity of solutions in the hypercube to a random 2-SAT problem.