The Constructions Of Mixed Covering Arrays On Hypergraphs

Mixed covering arrays are the extension of orthogonal arrays.The research of them is one of the hot problems in the field of combinatorics.Mixed covering arrays have wide applications in many areas,such as software testing,network communication,pharmaceutical industry.Recently,mixed covering arrays have been extended to graphs and hypergraphs by many scholars in order to enhance the flexibility of applications.The existence problem of optimal mixed covering arrays on hypergraphs is one of the most important topics in the field of combinatorial designs.In this thesis,we focus on the constructions and the existence of mixed covering arrays on hypergraphs.The first chapter mainly introduces the basic theories of hypergraphs and the definitions of mixed covering arrays on hypergraphs.We also summarize the research status of mixed covering arrays on hypergraphs.The second chapter researches the constructions of mixed covering arrays on hypergraphs and balanced mixed covering arrays on hypergraphs.The third chapter determines the existence of two kinds of optimal balanced mixed covering arrays on hypergraphs,and gives a kind of covering arrays on hypergraphs which are related with designs.