Polynomial representation for the expected length of minimal spanning trees

Abstract

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 apply it to express the first few coefficients in terms of the structure of the underlying graph; e.g. number of vertices, edges and cycles.