  We consider the minimum spanning tree problem on a weighted complete
bipartite graph $K_{n_R, n_B}$ whose $n=n_R+n_B$ vertices are random, i.i.d.
uniformly distributed points in the unit cube in $d$ dimensions and edge
weights are the $p$-th power of their Euclidean distance, with $p>0$. In the
large $n$ limit with $n_R/n \to \alpha_R$ and $0<\alpha_R<1$, we show that the
maximum vertex degree of the tree grows logarithmically, in contrast with the
classical, non-bipartite, case, where a uniform bound holds depending on $d$
only. Despite this difference, for $p<d$, we are able to prove that the total
edge costs normalized by the rate $n^{1-p/d}$ converge to a limiting constant
that can be represented as a series of integrals, thus extending a classical
result of Avram and Bertsimas to the bipartite case and confirming a conjecture
of Riva, Caracciolo and Malatesta.
