吳仕傑 C數學

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題名:	完全C邊混合超圖的著色多項式 The Chromatic Polynomial of A Mixed Hypergraph with Complete C-edges
作者:	吳仕傑
貢獻者:	張宜武吳仕傑
關鍵詞:	混合超圖分離-收縮法循環的 mixed hypergraph splitting-contraction algorithm circular
日期:	2007
上傳時間:	2009-09-17 13:48:14 (UTC+8)
摘要:	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.
參考文獻:	[1] Voloshin, V. (1993), The mixed hypergraphs, Comput. Sci. J. Moldova, 1, pp. 45-52. [2] Voloshin, V. and Voss, H.-J. (2000), Circular Mixed hypergraphs I: colorability and unique colorability, Congr. Numer., 144, pp. 207-219. [3] Voloshin, V. (2002), Coloring Mixed Hypergraphs: Theory, Algorithms and Applications, American Mathematical Society. [4] West, D.B. (2001), Introduction to Graph Theory, 2nd ed., Prentice Hall.
描述:	碩士國立政治大學應用數學研究所 94751011 96