Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the heterochromatic number of hypergraphs associated to geometric
  graphs and to matroids   The heterochromatic number hc(H) of a non-empty hypergraph H is the smallest
integer k such that for every colouring of the vertices of H with exactly k
colours, there is a hyperedge of H all of whose vertices have different
colours. We denote by nu(H) the number of vertices of H and by tau(H) the size
of the smallest set containing at least two vertices of each hyperedge of H.
For a complete geometric graph G with n > 2 vertices let H = H(G) be the
hypergraph whose vertices are the edges of G and whose hyperedges are the edge
sets of plane spanning trees of G. We prove that if G has at most one interior
vertex, then hc(H) = nu(H) - tau(H) + 2. We also show that hc(H) = nu(H) -
tau(H) + 2 whenever H is a hypergraph with vertex set and hyperedge set given
by the ground set and the bases of a matroid, respectively.

13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn