# Acyclic orientations with path constraints

Rosa M. V. Figueiredo; Valmir C. Barbosa; Nelson Maculan; Cid C. de Souza^{[1]}

- [1] Universidade Estadual de Campinas, Instituto de Computação, Caixa Postal 6176, 13084-971 Campinas - SP, Brazil;

RAIRO - Operations Research - Recherche Opérationnelle (2008)

- Volume: 42, Issue: 4, page 455-467
- ISSN: 0399-0559

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topRosa M. V. Figueiredo, et al. "Acyclic orientations with path constraints." RAIRO - Operations Research - Recherche Opérationnelle 42.4 (2008): 455-467. <http://eudml.org/doc/245017>.

@article{RosaM2008,

abstract = {Many well-known combinatorial optimization problems can be stated over the set of acyclic orientations of an undirected graph. For example, acyclic orientations with certain diameter constraints are closely related to the optimal solutions of the vertex coloring and frequency assignment problems. In this paper we introduce a linear programming formulation of acyclic orientations with path constraints, and discuss its use in the solution of the vertex coloring problem and some versions of the frequency assignment problem. A study of the polytope associated with the formulation is presented, including proofs of which constraints of the formulation are facet-defining and the introduction of new classes of valid inequalities.},

affiliation = {Universidade Estadual de Campinas, Instituto de Computação, Caixa Postal 6176, 13084-971 Campinas - SP, Brazil;},

author = {Rosa M. V. Figueiredo, Barbosa, Valmir C., Maculan, Nelson, Cid C. de Souza},

journal = {RAIRO - Operations Research - Recherche Opérationnelle},

keywords = {acyclic orientations; path constraints; combinatorial optimization problems; facets of polyhedra},

language = {eng},

number = {4},

pages = {455-467},

publisher = {EDP-Sciences},

title = {Acyclic orientations with path constraints},

url = {http://eudml.org/doc/245017},

volume = {42},

year = {2008},

}

TY - JOUR

AU - Rosa M. V. Figueiredo

AU - Barbosa, Valmir C.

AU - Maculan, Nelson

AU - Cid C. de Souza

TI - Acyclic orientations with path constraints

JO - RAIRO - Operations Research - Recherche Opérationnelle

PY - 2008

PB - EDP-Sciences

VL - 42

IS - 4

SP - 455

EP - 467

AB - Many well-known combinatorial optimization problems can be stated over the set of acyclic orientations of an undirected graph. For example, acyclic orientations with certain diameter constraints are closely related to the optimal solutions of the vertex coloring and frequency assignment problems. In this paper we introduce a linear programming formulation of acyclic orientations with path constraints, and discuss its use in the solution of the vertex coloring problem and some versions of the frequency assignment problem. A study of the polytope associated with the formulation is presented, including proofs of which constraints of the formulation are facet-defining and the introduction of new classes of valid inequalities.

LA - eng

KW - acyclic orientations; path constraints; combinatorial optimization problems; facets of polyhedra

UR - http://eudml.org/doc/245017

ER -

## References

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- [7] M. Grötschel, M. Jünger, and G. Reinelt, Facets of the linear ordering polytope. Math. Program. 33 (1985) 43–60. Zbl0577.05035MR809748
- [8] M. Grötschel, M. Jünger, and G. Reinelt, On the acyclic subgraph polytope. Math. Program. 33 (1985) 28–42. Zbl0577.05034MR809747
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