Geodesic
Non-Stanley bounds for network reliability
Journal of Algebraic Combinatorics, Tome 5 (1996) no. 1, pp. 13-36.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Suppose that each edge of a connected graph $G$ of order $n$ is independently operational with probability $p$; the $reliability$ of $G$ is the probability that the operational edges form a spanning connected subgraph. A useful expansion of the reliability is as $p ^{ n - 1}$ å $_{ i = 0} ^{ d} H _{ i} ( 1 - p ) ^{ i}$ p^n - 1 sumnolimits_i = 0^d H_i $left( 1 - p right)$^i } , and the Ball-Provan method for bounding reliability relies on Stanley's combinatorial bounds for the $H$-vectors of shellable complexes. We prove some new bounds here for the $H$-vectors arising from graphs, and the results here shed light on the problem of characterizing the $H$-vectors of matroids.$
Keywords: network reliability, H-vector, shellable complex, matroid, graph polynomial 
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     title = {Non-Stanley bounds for network reliability},
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Brown, Jason I.; Colbourn, Charles J. Non-Stanley bounds for network reliability. Journal of Algebraic Combinatorics, Tome 5 (1996) no. 1, pp. 13-36. http://geodesic.mathdoc.fr/item/JAC_1996__5_1_a3/