A classical result of Motzkin and Straus established the connection between the Lagrangian of a graph and its maximum cliques.Applying it,they gave a new proof of Turán’s theorem.This aroused the interests in st...A classical result of Motzkin and Straus established the connection between the Lagrangian of a graph and its maximum cliques.Applying it,they gave a new proof of Turán’s theorem.This aroused the interests in studying the connection between continuous optimization and extremal problems in combinatorics.In 2009,S.Rota Bulòand M.Pelillo extended the result of Motzkin-Straus to r-uniform hypergraphs.Recently,Johnston and Lu initiated the study of the Turán density of a non-uniform hypergraph.Polynomial optimization problems related to several types of non-uniform hypergraphs and its applications on Turán densities have also been studied.In this paper,we obtain a Motzkin-Straus type of results for all non-uniform hypergraphs.Applying it,we give an upper bound of the Turán density of a complete non-uniform hypergraph.展开更多
基金This paper is supported in part by National Natural Science Foundation of China(No.11931002).
文摘A classical result of Motzkin and Straus established the connection between the Lagrangian of a graph and its maximum cliques.Applying it,they gave a new proof of Turán’s theorem.This aroused the interests in studying the connection between continuous optimization and extremal problems in combinatorics.In 2009,S.Rota Bulòand M.Pelillo extended the result of Motzkin-Straus to r-uniform hypergraphs.Recently,Johnston and Lu initiated the study of the Turán density of a non-uniform hypergraph.Polynomial optimization problems related to several types of non-uniform hypergraphs and its applications on Turán densities have also been studied.In this paper,we obtain a Motzkin-Straus type of results for all non-uniform hypergraphs.Applying it,we give an upper bound of the Turán density of a complete non-uniform hypergraph.
