  In this paper we have given an algorithmic proof of an long standing
Barnette's conjecture (1969) that every 3-connected bipartite cubic planar
graph is hamiltonian. Our method is quite different than the known approaches
and it rely on the operation of opening disjoint chambers, bu using
spiral-chain like movement of the outer-cycle elastic-sticky edges of the cubic
planar graph. In fact we have shown that in hamiltonicity of Barnette graph a
single-chamber or double-chamber with a bridge face is enough to transform the
problem into finding specific hamiltonian path in the cubic bipartite graph
reduced. In the last part of the paper we have demonstrated that, if the given
cubic planar graph is non-hamiltonian then the algorithm which constructs
spiral-chain (or double-spiral chain) like chamber shows that except one vertex
there exists (n-1)-vertex cycle.
