完全偶图的一类(1,2)因子分解

A Class of (1,2)—Factorizations of a Complete Graph

图G的一个支撑子图F称为G的一个(1,2)因子,当F的每一个连通分支是路或圈.若G能够分解成边不交的(1,2)—因子的并,则称这样的并为G的一个(1,2)—因子分解.完全偶图Km,n存在具有最小边数和最大边数的(1,2)—因子,定理1和定理2给出了Km,n的上述(1,2)—因子分解.

A spanning subgraph F of a graph G is said to be a (1,2)-factor of G, if every connected component of F is a path or a cycle. If a graph G can be resolved into the union of (1,2)-factors whose sets of edges are disjointed, the union is said to be a factorization of G. The complete graph K m,n has (1,2)-factors with minimum and maximum edges , and the (1,2)-factorizations of K m,n are given by Theorem 1 and Theorem 2.