| 摘要: | 在本篇論文中，我們主要是探討一個完全三分圖Kp,q,r是否能分割成三角星狀圖(簡稱星狀圖)。
我們先獲得Kp,q,r可以分割成星狀圖的必要條件，同時利用拉丁方陣進而得到若Kp,q,r可以分割成星狀圖，則Knp,nq,nr亦可以分割成星狀圖，對於一些特殊型態的p、q、r，我們獲得Kp,q,r的星狀圖分割，同時我們將所有q為6的倍數且q>=r>=q/2、5q/2>=p>=q的Kq,q,r與Kp,q,q分割成星狀圖，最後我們給予K2n,2n,2n分割成循環星狀圖的建構法。
In this thesis, we mainly discuss whether the complete tripartite graph Kp,q,r can be decomposed into asteroidal graphs.
First we obtain the necessary condition of the decomposition of Kp,q,r into asteroidal graphs. By using latin square, we prove that if Kp,q,r can be decomposed into asteroidal graphs then Knp,nq,nr can do too. For the special values of p、q、r, we give the decompositions. We obtain that Kq,q,r and Kp,q,q can be decomposed into asteroidal graphs if q is multiple of 6 andq>=r>=q/2、5q/2>=p>=q. At last, we give a construction to get cyclic asteroidal graph decomposition of K2n,2n,2n. |
