Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Lagrangians of Hypergraphs Containing Dense Subgraphs   Motzkin and Straus established a remarkable connection between the maximum
clique and the Lagrangian of a graph in 1965. This connection and its
extensions were successfully employed in optimization to provide heuristics for
the maximum clique number in graphs. It is useful in practice if similar
results hold for hypergraphs. In this paper, we provide upper bounds on the
Lagrangian of a hypergraph containing dense subgraphs when the number of edges
of the hypergraph is in certain ranges. These results support a pair of
conjectures introduced by Y. Peng and C. Zhao (2012) and extend a result of J.
Talbot (2002). \keywords{Cliques of hypergraphs \and Colex ordering \and
Lagrangians of hypergraphs \and Polynomial optimization}

7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg