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In this paper, we investigate the polynomial integrand of an integral formulathat yields the expected length of the minimal spanning tree of a graph whoseedges are uniformly distributed over the interval [0, 1]. In particular, wederive a general formula for the coefficients of the polynomial and apply it toexpress the first few coefficients in terms of the structure of the underlyinggraph; e.g. number of vertices, edges and cycles.

Polynomial representation for the expected length of minimal spanning trees