在這篇論文中，我們利用分離－收縮法(splitting-contraction algorithm)獲得一個擁有完全C邊以及循環D邊特性的圖之著色多項式。 假如一個混合超圖在點集合上有主要的循環， 使得所有的C邊和D邊包含一個主循環(host cycle)的連接子圖， 則稱此圖為循環的(circular)。 對於每個l≧2， 所有連續l個點會形成一個D邊時， 我們把D記作D_l。 如此一來， 超圖(X,Φ,D_2)就是圖論中n個點的普通循環。
我們先觀察擁有完全C邊和循環D邊的超圖， 利用分離－收縮法的第一步， 找到遞迴關係式並且解它。 然後我們就推廣到一般完全C邊及循環D邊的超圖。 / In this thesis, we obtain the chromatic polynomial of a mixed hypergraph with complete C-edges and circular D-edges by using splitting-contraction algorithm. A mixed hypergraph H=(X,C,D) is called circular if there exists a host cycle on the vertex set X such that every C-edge and every D-edge induces a connected subgraph of the host cycle. For each l≧2, we denote D by D_l if and only if every l consecutive vertices of X form a D-edge. Thus the mixed hypergraph (X,Φ,D_2) is a simple classical cycle on n vertices.
We observe first a mixed hypergraph with complete C-edges and D_2. By the first step of the splitting-contraction algorithm, we can find out the recurrence relation and solve it. Then we generalize the mixed hypergraph with complete C-edges and circular D-edges.
| Identifer | oai:union.ndltd.org:CHENGCHI/G0094751011 |
| Creators | 吳仕傑 |
| Publisher | 國立政治大學 |
| Source Sets | National Chengchi University Libraries |
| Language | 英文 |
| Detected Language | English |
| Type | text |
| Rights | Copyright © nccu library on behalf of the copyright holders |
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