Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Motzkin-Straus Type of Results and Frankl-F\"uredi Conjecture for
  Hypergraphs   A remarkable connection between the order of a maximum clique and the
Graph-Lagrangian of a graph was established by Motzkin and Straus in 1965. This
connection and its extension were useful in both combinatorics and
optimization. Since then, Graph-Lagrangian has been a useful tool in extremal
combinatorics. In this paper, we give a parametrized Graph-Lagrangian for
non-uniform hypergraphs and provide several Motzkin-Straus type results for
nonuniform hypergraphs which generalize results from [1] and [2]. Another part
of the paper concerns a long-standing conjecture of Frankl-F\"uredi on
Graph-Lagrangians of hypergraphs. We show the connection between the
Graph-Lagrangian of $\{1, r_1, r_2, \cdots, r_l\}$-hypergraphs and $\{ r_1,
r_2, \cdots, r_l\}$-hypergraphs. Some of our results provide solutions to the
maximum value of a class of polynomial functions over the standard simplex of
the Euclidean space.

27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an