Abstract
Given a finite hypergraph H = ( V, E) and, for each e ϵ E, a collection of nonempty subsets π e of e, Möbius inversion is used to establish a recursive formula for the number of connected components of the hypergraph H = ( V, ∪ eϵE π e ). As shown elsewhere, this formula is an essential ingredient in the context of a certain divide-and-conquer strategy that allows us to define a dynamical programming scheme solving Steiner's problem for graphs in linear time (however, with a constant depending hyperexponentially on their tree width).
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