Non-Stanley bounds for network reliability

Journal of Algebraic Combinatorics

Volumn 5, Issue 1, 1996, Pages 13-36

  Brown, Jason I ^a   Colbourn, Charles J ^b  

^a DALHOUSIE UNIVERSITY   (Canada)

^b UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Graph polynomial; H vector; Matroid; Network reliability; Shellable complex

Indexed keywords

EID: 0012772460     PISSN: 09259899     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1022484229443     Document Type: Article

References (16)

1. M.O. Ball and J.S. Provan, "Bounds on the reliability polynomial for shellable independence systems," SIAM J. Alg. Disc. Meth. 3 (1982), 166-181.
2. L.J. Billera and C.W. Lee, "A proof of the sufficiency of McMullen's conditions for f-vectors of simplicial convex polytopes," J. Comb. Th. A 31 (1981), 237-255.
3. A. Björner, "Homology and Shellability," in Matroid Applications, N. White (Ed.), Cambridge University Press, Cambridge, 1992.
4. F.T. Boesch, A. Satyanarayana, and C.L. Suffel, "Least reliable networks and the reliability domination," IEEE Trans. Comm. 38 (1990), 2004-2009.
5. J.I. Brown and C.J. Colbourn, "A set system polynomial with colouring and reliability applications," SIAM J. Disc. Math. 1 (1988), 151-157.
6. J.I. Brown and C.J. Colbourn, "On the log concavity of reliability and matroidal sequences," Adv. Appl. Math. 15 (1994), 114-127.
7. J.I. Brown and C.J. Colbourn, "Roots of the reliability polynomial," SIAM J. Disc. Math. 5 (1992), 571-585.
8. J.I. Brown, C.J. Colbourn, and J.S. Devitt, "Network transformations and bounding network reliability," Networks 23 (1993), 1-17.
9. C.J. Colbourn, The Combinatorics of Network Reliability, Oxford Univ. Press, New York, 1987.
10. C.J. Colbourn and W.R. Pulleyblank, "Matroid Steiner Problems, the Tutte polynomial and network reliability," J. Comb. Th. B 47 (1989), 20-31.
11. T. Hibi, "Face number inequalities for matroid complexes and Cohen-Macaulay types of Stanley-Reisner rings of distributive lattices," Pacific J. Math. 154 (1992), 253-264.
12. F.S. Macaulay, "Some properties of enumeration in the theory of modular systems," J. Lond. Math. Soc. 26 (1927), 531-555.
13. R.P. Stanley, "Cohen-Macaulay complexes," in Higher Combinatorics, M. Aigner (Ed.), Reidel, 51-64, 1977.
14. R.P. Stanley, Combinatorics and Commutative Algebra, Birkhäuser, Boston, 1983.
15. W.T. Tutte, "A ring in graph theory," Proc. Cambridge Phil. Soc. 43 (1947), 26-40.
16. D.J.A. Welsh, Matroid Theory, Academic Press, London, 1976.