Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the hypercompetition numbers of hypergraphs   The competition hypergraph $C{\cH}(D)$ of a digraph $D$ is the hypergraph
such that the vertex set is the same as $D$ and $e \subseteq V(D)$ is a
hyperedge if and only if $e$ contains at least 2 vertices and $e$ coincides
with the in-neighborhood of some vertex $v$ in the digraph $D$. Any hypergraph
with sufficiently many isolated vertices is the competition hypergraph of an
acyclic digraph. The hypercompetition number $hk(\cH)$ of a hypergraph $\cH$ is
defined to be the smallest number of such isolated vertices.
  In this paper, we study the hypercompetition numbers of hypergraphs. First,
we give two lower bounds for the hypercompetition numbers which hold for any
hypergraphs. And then, by using these results, we give the exact
hypercompetition numbers for some family of uniform hypergraphs. In particular,
we give the exact value of the hypercompetition number of a connected graph.

37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin