Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graphs of Systoles on hyperbolic surfaces   Given a hyperbolic surface, the set of all closed geodesics whose length is
minimal form a graph on the surface, in fact a so-called fat graph, which we
call the systolic graph. We study which fat graphs are systolic graphs for some
surface (we call these admissible).
  There is a natural necessary condition on such graphs, which we call
combinatorial admissibility. Our first main result is that this condition is
also sufficient.
  It follows that a sub-graph of an admissible graph is admissible. Our second
major result is that there are infinitely many minimal non-admissible fat
graphs (in contrast, for instance, to the classical result that there are only
two minimal non-planar graphs).

32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
18
The categories of this paper are: econ