arête uv. X est supposé être variable Si le réseau appartient à la classe G(q, n 1 , n 2 ), alors on peut par exemple écrire que y t Xy ? ? 1 y 2 pour tout vecteur y. Ceci nous fournit un ensemble d'inégalités valides qui pourraient renforcer la relaxation courante. On peut faire de même en utilisant les valeurs propres ? n , µ 1 , µ n?1 . En effet, le Laplacien s'exprime linéairement par rapport à X puisque L = X ? D, avec D uv = ? v?u x uv, Signalons enfin que la séparation de ces inégalités valides, se fait par simple calcul des valeurs propres de la matrice X ou du Laplacien X ? D. [1] BAIOU, M., MAHJOUB, A.R : Steiner 2-arête connected subgraph polytopes on seriesparallel graphs. SIAM J. Discrete Math, pp.505-514, 1997. ,
The capacitated m-ringstar problem, Operations Research, vol.55, pp.147-1162, 2007. ,
On distance matrices and laplacians, Linear algebra and its applications, pp.193-209, 2005. ,
Some results of the index of unicyclic graphs. Linear algebra and its applications, pp.1048-1059, 2006. ,
Mathematical models of the delay constrained routing problem Algorithmic Opérations Resaearch, pp.94-103, 2006. ,
A superadditive approach to solve the minimum cost single path routing problem : Prelimanry results INOC, pp.67-71, 2003. ,
Routing of uncertain demands, Optimization and Engineering, vol.3, pp.283-313, 2005. ,
Design of survivable networks based on end to end rerouting, proceeding of DRCN2001, 2001. ,
Unicyclic components in random graphs, Journal of Physics A : Mathematical and General, vol.37, 2004. ,
Algebraic connectivity of trees with a pendant edge of infinite weight. Electronic journal of linear algebra, pp.175-186, 2005. ,
Harmonic ghraphs with small number of cycles, Discrete Mathematics, vol.265, pp.31-44, 2003. ,
On the spectral radius of unicyclic graphs with perfect mathings. Linear algebra and its applications, pp.237-250, 2003. ,
The number of maximal independent sets in connected triangle free graphs. Discrete Mathematics, pp.169-178, 1999. ,
Méthodes d'Optimisation Combinatoire, 1996. ,
Linear time algorithms to the minimum all-ones problem for unicyclic and bicyclic graphs. Discrete mathematics, pp.93-98, 2004. ,
On cycle cones and polyhedra, Linear Algebra Appl, vol.114115, pp.613-640, 1989. ,
A matching problem with side constraint, Discrete Mathematics, vol.29, pp.135-159, 1980. ,
Spectra of graphs, theory and application, 1980. ,
A new spectral method for determining the number of spanning trees. Publications de l'Institut Mathematique, pp.49-52, 1981. ,
On graphs with second largest eigenvalue does not exceed ( ? 5 ? 1)/2, Discrete Mathematics, vol.138, pp.213-227, 1995. ,
Old and new results on algebraic connectivity of graphs. Linear algebra and its applications, pp.53-73, 2006. ,
An upper bound on the sum of squares of degrees in a graph, Discrete Mathematics, vol.185, issue.1-3, pp.245-248, 1998. ,
DOI : 10.1016/S0012-365X(97)00213-6
Steiner k-edge connected subgraph polyhedra, Journal of Combinatorial Optimization, vol.4, issue.1, pp.131-144, 2000. ,
DOI : 10.1023/A:1009893108387
k-edge connected polyhedra on series-parallel graphs, Operations Research Letters, vol.19, issue.2, pp.71-78, 1996. ,
DOI : 10.1016/0167-6377(96)00015-6
Matching : a well-solved class of integer linear programs , In : Combinatorial Structures and Their Applications, Proceedings of the Galgary International Conference on Combinatorial Structures and Their Applications Gordon and Breach, pp.69-87, 1969. ,
On a composition of independence systems by circuitidentification, Journal Of Combiatorial Theory Ser. B, vol.53, pp.235-259, 1991. ,
URL : https://hal.archives-ouvertes.fr/hal-01134449
Computational Integer Programming and Cutting Planes, Handbooks in OR & MS, vol.12, 2005. ,
Solving the two-connected network with bounded meshes problem, Oper. Res, vol.48, pp.866-877, 2000. ,
The 2-edge connected subgraphs problem with bounded rings, Math. Prog, 2003. ,
Upper bound on algebraic connectivity via convex optimization . Linear algebra and its applications, pp.693-707, 2006. ,
Algebraic graph theory, Graduate texts in Mathematics, 2000. ,
Minimizing submodular functions over families of sets, 1993. ,
A general approximation technique for constrained forest problems, SIAM Journal on Computing, vol.24, pp.296-317, 1995. ,
A new approach to the maximum flow problem, Journal of the ACM, vol.35, pp.921-940, 1988. ,
Designing reliable tree networks with two cable technologies, European Journal of Operations Research, vol.105, pp.552-568, 1998. ,
Design of survivable networks. Handbook in Operations research and Management science, pp.617-671, 1995. ,
Polyderal approaches to networks survivability . Reliability of Computer and Communication Networks, DIMACS Ser. Discrete Math. Theoret. Comput. Sci, vol.55, pp.121-141, 1991. ,
Integer polyhedra arising from certain networks design problems with connectivity constraints, SIAM J. Discrete Maths, vol.3, pp.502-523, 1990. ,
On the symmetric travelling salesman problem I : inequalities. Mathematical Programming, pp.265-280, 1979. ,
On the symmetric travelling salesman problem II : lifting theorems and facets, Mathematical Programming, vol.16, pp.281-302, 1979. ,
Geometric Algorithms and Combinatorial Optimization, 1985. ,
Laplacian eigenvalues of growing trees. Department of mathematics ,
A sharp upper bound of the spectral radius of graphs, Journal of combinatorial theory, vol.81, pp.177-183, 2001. ,
Unicyclic graphs with maximal energy. Linear Algebra and its applications, pp.27-36, 2002. ,
Unicyclic graphs with exactly two main eigenvalues Applied mathematics letters, pp.1143-1147, 2005. ,
A combinatorial strongly polynomial time algorithm for minimizing submodular functions, Journal of the ACM, vol.48, pp.761-777, 2001. ,
Design of Survivable Networks : A survey, Networks, vol.46, pp.1-21, 2005. ,
On Survivable Network Polyhedra, Discrete Mathematics, vol.290, pp.183-210, 2005. ,
2)-survivable networks : facets and branch-and-cut.. The Sharpest Cut : The impact of Manfred Padberg and His Work, SIAM, Philadelphia, pp.121-152, 2004. ,
Combinatorial optimization : theory and algorithms, 2005. ,
A branch and cut algorithm for hub location problems with single assignment. Mathematical programming, pp.371-405, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-01255576
The ring star problem : polyhedral analysis and exact algorithm, Networks, vol.43, pp.177-189, 2004. ,
URL : https://hal.archives-ouvertes.fr/hal-01255584
Locating cycles in transportation and telecommunications networks, Networks, vol.50, pp.92-108, 2007. ,
On embedding ring into a star-related network Informatics and computer science, pp.21-35, 1997. ,
The Traveling Salesman Problem, Discrete Mathématics and Optimization, 1990. ,
Odd minimum cut-sets and b-matchings revisited, SIAM J. Discr. Math, vol.22, issue.4, pp.1480-1487, 2008. ,
Bounds of laplacian spectrum of graphs based on the domination number. Linear algebra and its applications, pp.390-396, 2005. ,
Lower bounds of the laplacian spectrum of graphs based on diameter. Linear algebra and its applications, pp.400-406, 2007. ,
Assigning spare capacities in survivable mesh networks. Telecommunications systems, pp.441-452, 2000. ,
Methods for designing communications networks with certain two-connected survivability constraints, Oper. Res, vol.37, pp.531-541, 1989. ,
A tutorial on Max-Min fairness and its applications to routing and load balacing in telecommunication networks ,
-Matchings, Mathematics of Operations Research, vol.7, issue.1, pp.67-80, 1982. ,
DOI : 10.1287/moor.7.1.67
URL : https://hal.archives-ouvertes.fr/hal-00761068
The number of independent sets in unicyclic graphs, Discrete Applied Mathematics, vol.152, issue.1-3, pp.246-256, 2005. ,
DOI : 10.1016/j.dam.2005.04.002
An approach to robust network design in telecommunications. RAIRO Operation research, pp.411-426, 2007. ,
A sharp upper bound on the largest eigenvalue of the laplacian matrix of a graph. Linear algebra and its applications, pp.123-129, 2002. ,
A simple min-cut algorithm, Journal of the ACM, vol.44, pp.585-591, 1997. ,
On the nullity and the matching number of unicyclic graphs ,
On the spectral radius of unicyclic graphs. Institute of systems science. Academy of mathematics and system sciences, 2003. ,
|S| = 70 à gauche, et S =, p.59 ,