Facets of the weak order polytope derived from the induced partition projection

SIAM Journal on Discrete Mathematics

Volumn 15, Issue 1, 2001, Pages 112-121

  Doignon, Jean Paul ^a   Fiorini, Samuel ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

Facet of convex polytope; Partition polytope; Weak order polytope

Indexed keywords

GRAPH THEORY; MAPPING; SET THEORY; THEOREM PROVING; VECTORS;

FACET OF CONVEX POLYTOPES; PARTITION POLYTOPES; WEAK ORDER POLYTOPES;

PROBLEM SOLVING;

EID: 0009914036     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895480100369936     Document Type: Article

References (13)

1. H.-J. BANDELT, M. OOSTEN, J. H. G. C. RUTTEN, AND F. C. R. SPIEKSMA. Lifting theorems and facet characterization for a class of clique partitioning inequalities, Oper. Res. Lett., 24 (1999), pp. 235-243.
2. J.-C. BERMOND, Ordres à distance minimum d'un tournoi et graphes partiels sans circuits maximaux, Math. Sci. Humaines, 37 (1972), pp. 5-25.
3. G. BOLOTASHVILI, M. KOVALEV, AND E. GIRLICH, New facets of the linear ordering polytope, SIAM J. Discrete Math., 12 (1999), pp. 326-336.
4. S. FIORINI, Determining the automorphism group of the linear ordering polytope, Discrete Appl. Math., 112 (2001), pp. 121-128.
5. S. FIORINI, Polyhedral Combinatorics of Order Polytopes, Ph.D. thesis, Université Libre de Bruxelles, Brussels, Belgium, 2001.
6. S. FIORINI AND P. FISHBURN. Weak order polytopes, submitted.
7. P. FISHBURN, Induced binary probabilities and the linear ordering polytope: A status report, Math. Social Sci., 23 (1992), pp. 67-80.
8. M. GRÖTSCHEL, M. JÜNGER, AND G. REINELT, Facets of the linear ordering polytope, Math. Programming, 33 (1985), pp. 43-60.
9. M. GRÖTSCHEL AND Y. WAKABAYASHI. Facets of the clique partitioning polytope, Math. Programming, 47 (1990), pp. 367-387.
10. M GURGEL, Poliedros de Grafos Transitivos, Ph.D. thesis, Instituto de Matemática e Estatística da Universidade de São Paulo, São Paulo, Brazil, 1992.
11. M GURGEL AND Y. WAKABAYASHI, The Complete Pre-order Polytope: Facets and Separation Problem, manuscript, 1996.
12. M. GURGEL AND Y. WAKABAYASHI, Adjacency of vertices of the complete pre-order polytope. Discrete Math., 175 (1997), pp. 163-172.
13. J.-F. LASLIER, Tournament Solutions and Majority Voting, Stud. Econom. Theory 7, Springer, Berlin. 1997.