Ten years of work on the Brown-Colbourn conjecture
University of Waterloo
refreshments at 3:45pm
The reliability polynomial $R(G;q)$ of a
(finite, connected, loopless, multi-) graph is the probability that if
each edge is deleted independently with probability $q$, then the
remaining spanning subgraph is still connected. In 1992, Brown and
Colbourn conjectured that every complex zero of the polynomial $R(G;q)$
lies in the closed unit disc $|q|\leq 1$. In this talk I will review
the progress which has been made towards understanding this conjecture
over the past decade, including work of Brown, Colbourn, Sokal,
Chari, Choe, Royle, and others. Possible generalizations to matroids,
and implications for the $f$--vectors of matroids will also be discussed.
Speaker's Contact Info: dgwagner(at-sign)pythagoras.math.uwaterloo.ca
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