Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T23:33:04.382Z Has data issue: false hasContentIssue false
  • English
  • Français

Clique-connecting forest and stable set polytopes

Published online by Cambridge University Press:  08 February 2010

Denis Cornaz
Denis Cornaz*
Affiliation:
LIMOS, Complexe scientifique des Cézeaux, 63177 Aubiere Cedex, France; cornaz@isima.fr
Get access

Abstract

Let G = (V,E) be a simple undirected graph.A forest F ⊆ E of G is said to be clique-connecting if each tree of F spans a clique of G.This paper adresses the clique-connecting forest polytope.First we give a formulation and a polynomial time separation algorithm. Then we show that the nontrivial nondegenerate facets of the stable set polytope are facets of the clique-connecting polytope.Finally we introduce a family of rank inequalities which are facets, and which generalize the clique inequalities.

Keywords

Graphpolytopeseparationfacet
Type
Research Article
Information
RAIRO - Operations Research , Volume 44 , Issue 1 , January 2010 , pp. 73 - 83
Copyright
© EDP Sciences, ROADEF, SMAI, 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Campêlo, M., Corrêa, R. and Frota, Y., Cliques, holes and the vertex coloring polytope. Inf. Process. Lett. 89 (2004) 159–164. CrossRef
Cornaz, D. and Jost, V., A one-to-one correspondence beetween stables sets and colorings. Oper. Res. Lett. 36 (2008) 673–676. CrossRef
Cheng, E. and Cunningham, W.H., Wheel inequalitites for stable set polytopes. Math. Program. 77 (1997) 389–421.
Edmonds, J., Maximum matching and a polyhedron with 0,1-vertices. Journal of Resarch National Bureau of Standards Section B 69 (1965) 67–72. CrossRef
Edmonds, J., Matroids and the greedy algorithm. Math. Program. 1 (1971) 127–136. CrossRef
Grötschel, M., Lovàsz, L. and Schrijver, A., The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1 (1981) 169–197. CrossRef
Padberg, M.W., On the facial structure of set packing polyhedra. Math. Program. 5 (1973) 199–215. CrossRef
Padberg, M.W. and Wolsey, L.A., Fractional covers for forests and matchings. Math. Program. 29 (1984) 1–14. CrossRef
Picard, J.-C. and Queyranne, M., Selected applications of minimum cuts in networks. INFOR Can. J. Oper. Res. Inf. Process. 20 (1982) 394–422.
Rhys, J.M.W., A selection problem of shared fixed costs and network flows. Manag. Sci. 17 (1970) 200–207. CrossRef
A. Schrijver, Combinatorial Optimization. Springer-Verlag, Berlin, Heidelberg (2003).