  Ge and Stefankovic have recently introduced a novel two-variable graph
polynomial. When specialised to a bipartite graphs G and evaluated at the point
(1/2,1) this polynomial gives the number of independent sets in the graph.
Inspired by this polynomial, they also introduced a Markov chain which, if
rapidly mixing, would provide an efficient sampling procedure for independent
sets in G. This sampling procedure in turn would imply the existence of
efficient approximation algorithms for a number of significant counting
problems whose complexity is so far unresolved. The proposed Markov chain is
promising, in the sense that it overcomes the most obvious barrier to mixing.
However, we show here, by exhibiting a sequence of counterexamples, that the
mixing time of their Markov chain is exponential in the size of the input when
the input is chosen from a particular infinite family of bipartite graphs.
