摘要
A remarkable connection between the clique number and the Lagrangian of a graph was established by Motzkin and Straus. Later, Rota Bul′o and Pelillo extended the theorem of Motzkin-Straus to r-uniform hypergraphs by studying the relation of local（global） minimizers of a homogeneous polynomial function of degree r and the maximal（maximum） cliques of an r-uniform hypergraph. In this paper, we study polynomial optimization problems for non-uniform hypergraphs with four different types of edges and apply it to get an upper bound of Tur′an densities of complete non-uniform hypergraphs.
A remarkable connection between the clique number and the Lagrangian of a graph was established by Motzkin and Straus. Later, Rota Bul′o and Pelillo extended the theorem of Motzkin-Straus to r-uniform hypergraphs by studying the relation of local（global） minimizers of a homogeneous polynomial function of degree r and the maximal（maximum） cliques of an r-uniform hypergraph. In this paper, we study polynomial optimization problems for non-uniform hypergraphs with four different types of edges and apply it to get an upper bound of Tur′an densities of complete non-uniform hypergraphs.
基金
Supported by the National Natural Science Foundation of China(No.11671124)
