Feasible Bases for a Polytope Related to the Hamilton Cycle Problem

We study a certain polytope depending on graph $G$ and parameter $\beta\in(0,1)$ which arises from embedding the Hamiltonian cycle problem in discounted Markov decision process. Eshragh \emph{et al.} conjectured lower bound proportion of feasible bases corresponding to cycles set all bases. make progress towards proof conjecture by proving results about structure In particular, we prove three main results: (1) is independent $\beta$ when close 1, (2) can be interpreted as generalized network flow (3) deduce combinatorial interpretation also provide full characterization for special class bases, apply this some computational support conjecture.