Chromatic, Flow and Reliability Polynomials: The Complexity of their Coefficients
Combinatorics, Probability and Computing
Zeros of Reliability Polynomials and f-vectors of Matroids
Combinatorics, Probability and Computing
Chip firing and all-terminal network reliability bounds
Discrete Optimization
PReach: Reachability in Probabilistic Signaling Networks
Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics
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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} \sum_{i=0}^d\ H_i(1 \ - \ p)^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.