  Given an undirected graph $G(V, E)$, it is well known that partitioning a
graph $G$ into $q$ connected subgraphs of equal or specificed sizes is in
general NP-hard problem. On the other hand, it has been shown that the
q-partition problem is solvable in polynomial time for q-connected graphs. For
example, efficient polynomial time algorithms for finding 2-partition
(bipartition) or 3-partition of 2-connected or 3-connected have been developed
in the literature. In this paper, we are interested in the following problem:
given a bi-connected graph $G$ of size $n$, can we partition it into two
(connected) sub-graphs, $G[V_1]$ and $G[V_2]$ of sizes $n_1$ and $n_2$ such as
both $G[V_1]$ and $G[V_2]$ are also bi-connected (and $n_1+n_2=n$)? We refer to
this problem as the recursive bipartition problem of bi-connected graphs,
denoted by R-BBG$_2$. We show that a ploynomial algorithm exists to both decide
the recursive bipartion problem R-BBG$_2$ and find the corresponding
bi-connected subgraphs when such a recursive bipartition exists.
