Total dual integrality of matching forest constraints

Combinatorica

Volumn 20, Issue 4, 2000, Pages 575-588

  Schrijver, Alexander ^a,b  

^a CWI   (Netherlands)

^b UNIVERSITY OF AMSTERDAM   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034366499     PISSN: 02099683     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004930070009     Document Type: Article

References (19)

1. F. BOCK: An algorithm to construct a minimum directed spanning tree in a directed network, in: Developments in Operations Research, Volume 1 (Proceedings of the Third Annual Israel Conference on Operations Research, Tel Aviv, 1969; B. Avi-Itzhak, ed.), Gordon and Breach, New York, 1971, 29-44.
2. YOENG-JIN CHU, TSENG-HONG LIU: On the shortest arborescence of a directed graph, Scientia Sinica [Peking] 14 (1965), 1396-1400.
3. W. H. CUNNINGHAM, A. B. MARSH, III: A primal algorithm for optimum matching, [in: Polyhedral Combinatorics - Dedicated to the Memory of D. R. Fulkerson (M. L. Balinski, A. J. Hoffman, eds.)] Mathematical Programming Study, 8 (1978), 50-72.
4. J. EDMUNDS: Maximum matching and a polyhedron with 0,1-vertices, Journal of Research National Bureau of Standards Section B, 69 (1965), 125-130.
5. J. EDMONDS: Optimum branchings, Journal of Research National Bureau of Standards Section B, 71 (1967), 233-240. [reprinted in: Mathematics of the Decision Sciences Part 1 (Proceedings Fifth Summer Seminar on the Mathematics of the Decision Sciences, Stanford, California, 1967; G. B. Dantzig, A. F. Veinott, Jr, eds.) [Lectures in Applied Mathematics Vol. 11], American Mathematical Society, Providence, Rhode Island, 1968, 346-361].
6. J. EDMONDS: Optimum branchings, Journal of Research National Bureau of Standards Section B, 71 (1967), 233-240. [reprinted in: Mathematics of the Decision Sciences Part 1 (Proceedings Fifth Summer Seminar on the Mathematics of the Decision Sciences, Stanford, California, 1967; G. B. Dantzig, A. F. Veinott, Jr, eds.) [Lectures in Applied Mathematics Vol. 11], American Mathematical Society, Providence, Rhode Island, 1968, 346-361].
7. J. EDMONDS: Optimum branchings, Journal of Research National Bureau of Standards Section B, 71 (1967), 233-240. [reprinted in: Mathematics of the Decision Sciences Part 1 (Proceedings Fifth Summer Seminar on the Mathematics of the Decision Sciences, Stanford, California, 1967; G. B. Dantzig, A. F. Veinott, Jr, eds.) [Lectures in Applied Mathematics Vol. 11], American Mathematical Society, Providence, Rhode Island, 1968, 346-361].
8. J. EDMONDS: Edge-disjoint branchings, in: Combinatorial Algorithms (Courant Computer Science Symposium 9, Monterey, California, 1972; R. Rustin, ed.), Algorithmics Press, New York, 1973, 91-96.
9. J. EDMONDS, R. GILES: A min-max relation for submodular functions on graphs, in: Studies in Integer Programming (Proceedings Workshop on Integer Programming, Bonn, 1975; P. L. Hammer, E. L. Johnson, B. H. Korte, G. L. Nemhauser, eds.) [Annals of Discrete Mathematics 1], North-Holland, Amsterdam, 1977, 185-204.
10. J. EDMONDS, R. GILES: A min-max relation for submodular functions on graphs, in: Studies in Integer Programming (Proceedings Workshop on Integer Programming, Bonn, 1975; P. L. Hammer, E. L. Johnson, B. H. Korte, G. L. Nemhauser, eds.) [Annals of Discrete Mathematics 1], North-Holland, Amsterdam, 1977, 185-204.
11. D. R. FULKERSON: Packing rooted directed cuts in a weighted directed graph, Mathematical Programming, 6 (1974), 1-13.
12. R. GILES: Optimum matching forests I: special weights, Mathematical Programming, 22 (1982), 1-11.
13. R. GILES: Optimum matching forests II: general weights, Mathematical Programming, 22 (1982), 12-38.
14. R. GILES: Optimum matching forests III: facets of matching forest polyhedra, Mathematical Programming, 22 (1982), 39-51.
15. L. LOVÁSZ: Graph theory and integer programming, in: Discrete Optimization (Proceedings Advanced Research Institute on Discrete Optimization and Systems Applications and Discrete Optimization Symposium, Banff, Alta, and Vancouver, B.C., Canada, 1977; P. L. Hammer, E. L. Johnson, B. H. Korte, eds.) [Annals of Discrete Mathematics 4], North-Holland, Amsterdam, 1979, 141-158.
16. L. LOVÁSZ: Graph theory and integer programming, in: Discrete Optimization (Proceedings Advanced Research Institute on Discrete Optimization and Systems Applications and Discrete Optimization Symposium, Banff, Alta, and Vancouver, B.C., Canada, 1977; P. L. Hammer, E. L. Johnson, B. H. Korte, eds.) [Annals of Discrete Mathematics 4], North-Holland, Amsterdam, 1979, 141-158.
17. L. LOVÁSZ, M. D. PLUMMER: Matching Theory, Akadémiai Kiadó, Budapest [also: North-Holland Mathematics Studies Volume 121, North-Holland, Amsterdam], 1986.
18. A. SCHRIJVER: Min-max results in combinatorial optimization, in: Mathematical Programming - The State of the Art (Bonn, 1982; A. Bachem, M. Grötschel, B. Korte, eds.), Springer, Berlin, 1983, 439-500.
19. A. SCHRIJVER: Theory of Linear and Integer Programming, Wiley, Chichester, 1986.