The dominant of the 2-connected-Steiner-subgraph polytope for W4-free graphs

Discrete Applied Mathematics

Volumn 66, Issue 1, 1996, Pages 33-43

  Coullard, Collette R ^a   Rais, Abdur ^b   Rardin, Ronald L ^c   Wagner, Donald K ^d  

^a Northwestern University   (United States)

^b BALL STATE UNIVERSITY   (United States)

^c SCHOOL OF INDUSTRIAL ENGINEERING   (United States)

^d OFFICE OF NAVAL RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042305305     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0166-218X(94)00135-Z     Document Type: Article

References (22)

1. 4 minor, SIAM J. Discrete Math. 7 (1994) 372-389.
2. F. Barahona and A.R. Mahjoub, On two-connected subgraph polytopes, unpublished manuscript (1991).
3. J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (North-Holland, New York, 1976).
4. N. Christofides and C.A. Whitlock, Network synthesis with connectivity constraints-a survey, in: J.P. Brans, ed., Operational Research' 81 (North-Holland, Amsterdam, 1981) 705-723.
5. C.R. Coullard, A. Rais, R.L. Rardin and D.K. Wagner, The 2-connected-spanning-subgraph polytope for series-parallel graphs, Report No. 90-12, School of Industrial Engineering, Purdue University (1990).
6. C.R. Coullard, A. Rais, R.L. Rardin and D.K. Wagner, The 2-connected-Steiner-subgraph polytope for series-parallel graphs, Report No. 91-23, School of Industrial Engineering, Purdue University (1991).
7. C.R. Coullard, A. Rais, R.L. Rardin, and D.K. Wagner, Linear-time algorithms for the 2-connected Steiner subgraph problem on special classes of graphs, Networks 23 (1993) 195-206.
8. R.J. Duffin, The extremal length of a network, J. Math. Anal. Appl. 5 (1962) 200-215.
9. R.J. Duffin, Topology of series-parallel networks, J. Math. Anal. Appl. 10 (1965) 303-318.
10. D.R. Fulkerson, Networks, frames, blocking systems, in: G.B. Dantzig and A.F. Veinott Jr., eds., Mathematics of Decision Sciences, Part 1. Lectures in Applied Mathematics, Vol. 11 (American Mathematical Society, Providence, RI, 1968) 303-334.
11. H. Gan and E.L. Johnson, Four problems on graphs with excluded minors, Math. Programming 45 (1989) 311-330.
12. M. Grötschel and C.L. Monma, Integer polyhedra associated with certain network design problems with connectivity constraints, SIAM J. Discrete Math. 3 (1990) 502-523.
13. M. Grötschel, C.L. Monma and M. Stoer, Polyhedral approaches to network survivability, in: DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 5 (AMS, New York, 1991) 121-141.
14. M. Grötschel, C.L. Monma and M. Stoer, Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints, Oper. Res. 40 (1992) 309-330.
15. A.R. Mahjoub, Two edge connected spanning subgraphs and polyhedra, Report No. 88520-OR, Institute for Operations Research, University of Bonn (1988).
16. C.L. Monma, B.S. Munson and W.R. Pulleyblank, Minimum-weight two-connected spanning networks, Math. Programming 46 (1990) 153-172.
17. C.L. Monma and D.F. Shallcross, Methods for designing communication networks with certain two-connected survivability constraints, Oper. Res. 37 (1989) 531-541.
18. G.L. Nemhauser and L.A. Wolsey, Integer and Combinatorial Optimization (Wiley, New York, 1988).
19. A. Rais, A polytope and its dominant, Report No. 91-24, School of Industrial Engineering, Purdue University (1991).
20. A. Schrijver, Theory of Linear and Integer Programming (Wiley, Chichester, 1986).
21. W.T. Tutte, Connectivity in Graphs (Univ. Toronto Press, Toronto, 1966).
22. P. Winter, Generalized Steiner problem in series-parallel networks, J. Algorithms 7 (1986) 549-566.