### Abstract

We prove the conjecture formulated in the paper by N. Litvak and V. Ejov ("Markov Chains and Optimality of The Hamiltonian Cycle", to appear in Math. Oper. Res., 2008), namely, that the trace of the fundamental matrix of a singularly perturbed Markov chain is minimized at policies corresponding to Hamiltonian cycles, over the set of all stochastic policies feasible for a given graph.

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | Stochastic Operations Research (SOR) |

Number of pages | 10 |

Publication status | Published - Jun 2008 |

### Publication series

Name | |
---|---|

Publisher | Department of Applied Mathematics, University of Twente |

No. | 274/1869 |

ISSN (Print) | 1874-4850 |

ISSN (Electronic) | 1874-4850 |

### Keywords

- IR-64811
- METIS-251008
- MSC-11C20
- MSC-05C45
- MSC-60J10
- EWI-12877

## Cite this

Ejov, V., Litvak, N., & Nguyen, G. (2008).

*Proof of the Hamiltonicity-Trace conjecture for singularly perturbed Markov chains*. Enschede: Stochastic Operations Research (SOR).