  In this paper we propose a new approach for developing a proof that P=NP. We
propose to use a polynomial-time reduction of a NP-complete problem to Linear
Programming. Earlier such attempts used polynomial-time transformation which is
a special form of reduction that uses a subroutine for the easier Linear
Programming Problem only once. We use multiple calls to the subroutine
increasing considerably the effectiveness of the reduction. Further the
NP-complete problem we choose is also unusual. We define a special kind of
acyclic directed graph which we call a time graph. We define Hamiltonian time
paths in such graphs and also the Hamiltonian Time Path problem (HTPATH) and
prove that it is NP-complete. We then state a conjecture whose proof will
immediately lead to a polynomial-time algorithm for this problem proving P=NP.
