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| 研究生： |
游朝凱 |
|---|---|
| 論文名稱： |
圖之和弦圖數與樹寬 The Chordality and Treewidth of a Graph |
| 指導教授： | 張宜武 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系數學教學碩士在職專班 |
| 論文出版年： | 2011 |
| 畢業學年度： | 100 |
| 語文別： | 英文 |
| 論文頁數： | 42 |
| 中文關鍵詞： | 和弦圖數 、樹寬 、樹分解 、系列平行圖 |
| 外文關鍵詞： | Chordality, Treewidth, Tree Decomposition, Series Parallel Graph |
| 相關次數： | 點閱：284 下載：10 |
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對於任何一個圖G = (V;E) ，如果我們可以找到最少的k 個弦圖(V;Ei)，使得E = E1 \ \ Ek ，則我們定義此圖G = (V;E) 的chordality為k ；而一個圖G = (V;E) 的樹寬則被定義為此圖所有的樹分解的寬的最小值。在這篇論文中，最主要的結論是所有圖的chordality 會小於或等於它的樹寬；更特別的是，有一些平面圖的chordality 為3，而所有系列平行圖的chordality 頂多為2。
The chordality of a graph G = (V;E) is de ned as the minimum k such that we can write E = E1 \ \ Ek, where each (V;Ei) is a chordal graph. The treewidth of a graph G = (V;E) is de ned to be the minimum width over all tree decompositions of G. In this thesis, the principal result is that the chordality of a graph is at most its treewidth. In particular, there are planar graphs with chordality 3, and series-parallel graphs have chordality at most 2.
Abstract ii
中文摘要iii
1 Introduction 1
1.1 History of Chordality and Treewidth 1
1.2 The De nition of Chordality and Treewidth 2
2 The Chordality of a Graph 6
2.1 Theorems and Examples of Chordality 6
2.2 The Counter Example 14
3 The Treewidth of a Graph 15
3.1 The Treewidth of Some Classes of Graphs 15
3.2 The Chordality of K2;2;2 22
4 Chordality vs. Treewidth 23
4.1 The Weaker Inequality between Chordality and Treewidth 23
4.2 Chordality Bounded by Its Treewidth 24
4.3 The Chordality of Series{Parallel Graphs 37
References 38
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