E. Balas and M. Oosten, On the cycle polytope of a directed graph. Networks, pp.34-46, 2000.

E. Balas and R. Stephan, On the cycle polytope of a directed graph and its relaxations. Networks, pp.47-55, 2009.

P. Bauer, A Polyhedral Approach to the Weighted Girth Problem. Dissertation, Institut fur informatik, 1994.

D. Coppersmith and S. Winograd, Matrix multiplication via arithmetic progressions, Proceedings of the nineteenth annual ACM conference on Theory of computing , STOC '87, pp.251-280, 1990.
DOI : 10.1145/28395.28396

C. Coullard and W. R. Pulleyblank, On cycle cones and polyhedra, Linear Algebra and its Applications, vol.114, issue.115, pp.613-640, 1989.
DOI : 10.1016/0024-3795(89)90483-7

S. Fortune, J. Hopcroft, and J. Wyllie, The directed subgraph homeomorphism problem, Theoretical Computer Science, vol.10, issue.2, pp.111-121, 1980.
DOI : 10.1016/0304-3975(80)90009-2

V. Kaibel and R. Stephan, On cardinality constrained cycle and path polytopes, Mathematical Programming, vol.8, issue.2, 2007.
DOI : 10.1007/s10107-008-0257-2

M. S. Ibrahim, N. Maculan, and H. Ouzia, A new class of valid inequalities for the minimum weighted elementary directed cycle problem in digraph

M. S. Ibrahim, N. Maculan, and M. Minoux, A note on the NP-hardness of the separation problem on some valid inequalities for the elementary shortest path problem, Pesquisa Operacional, vol.34, issue.1, pp.117-124, 2014.
DOI : 10.1590/S0101-74382014000100009

M. S. Ibrahim, N. Maculan, and M. Minoux, A strong flow-based formulation for the shortest path problem in digraphs with negative cycles, International Transactions in Operational Research, vol.13, issue.3, pp.361-369, 2009.
DOI : 10.1111/j.1475-3995.2008.00681.x

M. S. Ibrahim, N. Maculan, and M. Minoux, Valid inequalities and lifting procedures for the shortest path problem in digraphs with negative cycles. Optimization letters, pp.345-357, 2015.

A. Itai and M. Rodeh, Finding a Minimum Circuit in a Graph, SIAM Journal on Computing, vol.7, issue.4, pp.413-423, 1978.
DOI : 10.1137/0207033

A. N. Letchford and N. A. Pearson, A fast algorithm for minimum weight odd circuits and cuts in planar graphs, Operations Research Letters, vol.33, issue.6, pp.625-628, 2005.
DOI : 10.1016/j.orl.2004.12.001

A. Lingas and E. Lundell, Efficient approximation algorithms for shortest cycles in undirected graphs, Information Processing Letters, vol.109, issue.10, pp.493-498, 2009.
DOI : 10.1016/j.ipl.2009.01.008

N. Maculan, G. Plateau, and A. Lisser, Integer linear models with a polynomial number of variables and constraints for some classical combinatorial optimization problems, Pesquisa Operacional, vol.23, issue.1, pp.161-168, 2003.
DOI : 10.1590/S0101-74382003000100012

M. Minoux and H. Ouzia, DRL*: A hierarchy of strong block-decomposable linear relaxations for 0???1 MIPs, Discrete Applied Mathematics, vol.158, issue.18, pp.2031-2048, 2010.
DOI : 10.1016/j.dam.2010.08.020
URL : https://hal.archives-ouvertes.fr/hal-01170343

L. Roditty and V. V. Williams, Minimum Weight Cycles and Triangles: Equivalences and Algorithms, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, pp.180-189, 2011.
DOI : 10.1109/FOCS.2011.27

R. Yuster and U. Zwick, Finding Even Cycles Even Faster, SIAM Journal on Discrete Mathematics, vol.10, issue.2, pp.209-1227, 1997.
DOI : 10.1137/S0895480194274133