The Independence Numbers Of The Tensor Products Of Vertex-transitive Graphs

Combinatorics is an important branch of mathematics.The extremal combinatirica is a very important type of combinatorial research.In 1928,the Sperner theorem proposed by Sperner opened the prelude to Sperner theory.Because Sperner theory is widely used,it attracts many scholars to study it.It developed rapidly,and eventually developed into a systematic theory.Among them,the EKR theorem is also a famous theorem,it was published by Erd?os-Ko-Rado in 1961 is a generalization of Sperner theorem.EKR theorem is a main theorem in extremal combinatirica,and it mainly studies the properties of set intersections.It is the earliest results of the study of finite intersection families,it is also the classic conclusions in extremal combinatirica.With scholars for decades research,the EKR theorem has been generalized in various forms.However,there are still many problems with the properties of the intersection of EKR properties to study.This article continues to study the type of EKR problems of graphs,we mainly study independent sets in tensor product.The first chapter of this article,we first introduce the source of the EKR theorem and generalizations of the EKR theorem.In the second chapter,we mainly determine the independence numbers of the tensor product of any two vertex-transitive graphs and a circle graph,and characterize the structure of their maximum independent sets.In the last chapter,we mainly determine the independence numbers of the tensor product of any two vertex-transitive graphs and a Kneser graph,and characterize the structure of their maximum independent sets.