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A homogeneous polynomial associated with general hypergraphs and its applications

2018-12-01
 

Academic Report

Title: A homogeneous polynomial associated with general hypergraphs and its applications

Reporter: Prof. CHANG An (Fuzhou University)

Time: December 2, 2018 (Sunday) PM 14:00-15:00

Location: A1101# room, Innovation Park Building

Contact: prof. WANG Yi (tel:84708351-8128)

 

Abstract: In 1965, Motzkin and Straus established a remarkable connection betweenthe order of a maximum clique and a homogeneous polynomial of a graph in the last decade, the tensor spectral theory of hypergraphs has been well developed due to its retical significance and applications in many d A general hypergraph is apair H=(, E) consisting of a vertex set V and an edge set E which is a collection of subsets of V. The rank of H, denoted by rank (H), is the maximum cardinality of the edges in E. In this talk, we first define a homogeneous polynomial for a general hypergraph, and t Hen give a Motzkin-straus type result for m, m-1) hypergraphs with hrank M. We also give some lower and upper bounds on the spectral radius in terms of the clique number. This is the joint work with Yuan Hou and Lei Zhang.

 

The brief introduction to the reporter: Chang'an is a professor and doctoral supervisor in the School of Mathematics and Computer Science, Fuzhou University. He graduated from Qinghai Normal University in June 1983 with a bachelor's degree, Xinjiang University in 1990 with a master's degree, and Sichuan University in June 1998 with a doctorate. He is mainly engaged in the basic theoretical research of algebraic graph theory and chemical graph theory in the field of graph theory. He has participated in many research projects of the National Fund. He is currently the main research member of the project group of the National Fund Committee's key projects and the 973 project of the National Key Research Plan, and presides over the research work of a National Natural Science Foundation project. In 1995, he won the third prize for scientific and technological progress in Qinghai Province and the second prize for science and technology in Fujian Province in 2004.