Polynomial Representation for the Expected Length of Minimal Spanning Trees∗

In this paper, we investigate the polynomial integrand of an integral formula that yields the expected length of the minimal spanning tree of a graph whose edges are uniformly distributed over the interval [0, 1]. In particular, we derive a general formula for the coefficients of the polynomial and use it to express the first few coefficients in terms of the structure of the underlying graph; e.g. number of vertices, edges and cycles.