Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Minimum Spanning Trees for Random Euclidean Bipartite Graphs   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.

30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat