In case of primal degeneracy, instead, you have a (possibly
exponential) n. of different bases B*_1, B*_2, .... associated with a
single vertex x*, and each such basis can produce up to n-m adjacent
vertices, meaning that the total number of adjacent vertices can
explode. In other words, if x is vertex geometrically adjacent to
x*, you can still reach x through a single pivot from a CERTAIN basis
B*_k associated with x*, but you have to try all possible such bases
B*_1, B^*_2, ... to find the B*_k that works.