完全图K_n(完全二部图K_(n,n))的一个k-匹配的集合〖KX(〗M〖KX)〗,若满足:K_n(K_(n,n))的每一对独立边恰出现在〖KX(〗M〖KX)〗的λ个元素中,则称〖KX(〗M〖KX)〗为一个匹配设计,记为MATCH(n,k,λ)(BIMATCH(n,k,λ))-设计.该文定义两个匹配设计对应的矩阵,并以此构造出某些新的匹配设计.

Alspach and Heinrich introduced the concept of matching designs.A matching design denoted by MATCH(n,k,λ)-design is a family of k-matchings(i.e. k independent edges) of K_n so that every pair of independent edges lie in exactly λ members of the k-matchings.An analogous definition is given for bipartite graph K_(n,n),and the corresponding design is called a BIMATCH(n,k,λ)-design.In this paper,we define the matrices corresponding to the matching designs,prove the existence of MATCH(n,k,λ) and BIMATCH(n,k,λ)-designs,and at the same time give their constructions.