完全多部图Kn(t)的{K3+e}分解

如果Kn(t)能分解成一族同构于G的边不交的子图的集合，那么称Kn(t)存在G分解，讨论了当G是K3 e时，Kn(t)的G分解的存在性并给出其充要条件是：参数n，t满足下列条件之一：(1)t为偶数且n≥3；(2)t为奇数且n≡0，1(mod8)。

{K3+e}-Decomposition of Complete Multigraphs Kn(t)

The complete multigraphs Kn(t) is said to have a G-decomposition,if it is the union of edge disjoint subgraphs each isomorphic to G. In this paper, G-decomposition of Kn(t) where G is the triangle with attached edge is studied. Necessary and sufficient conditions are given for the G-decomposition of Kn(t). The graph Kn(t) can be decomposed into G if and only if one of following conditions holds:(1) n≥3, when t≡0(mod 2);(2) n≡0,1 (mod 8), when t≡1(mod 2).