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題名 圖之和弦圖數與樹寬
The Chordality and Treewidth of a Graph作者 游朝凱 貢獻者 張宜武
游朝凱關鍵詞 和弦圖數
樹寬
樹分解
系列平行圖
Chordality
Treewidth
Tree Decomposition
Series Parallel Graph日期 2011 上傳時間 10-May-2016 19:33:38 (UTC+8) 摘要 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 dened 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 dened 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 38參考文獻 [1] L.W. Beineke and R.E. Pippert, Properties and characterizations of k-trees, Mathematika, 18 (1971), 141-151. [2] P. Bumeman, A characterization of rigid circuit graphs, Discrete Mathematics, 9 (1974), 205-212. [3] M.B. Cozzens and F.S. Roberts, On dimensional properties of graphs, Graphs and Combinatorics, 5 (1989), 29-46. [4] G.A. Dirac, A property of 4-chromatic graphs and some remarks on critical graphs, J. London Math. Soc., 27 (1952), 85-92. [5] R.J. Dun, Topology of series parallel-networks, J. Math. Anal. Appl., 10 (1965), 303-318. [6] F. Gavril, The intersection graphs of subtrees in trees are exactly the chordal graphs, Journal of Combinatorial Theory (B), 16 (1974), 47-56. [7] Pinar Heggernes, Treewidth, partial k-trees, and chordal graphs, Delpensum INF 334- Institutt for informatikk, (2006). [8] Terry A. McKee and Edward R. Sceinerman, On the Chordality of a Graph, Journal of Graph Theory, 17 (1993), 221-232. [9] H.P. Patil, On the structure of k{trees, J. Combin. Inform. System. Sci., 11 (1986), 57-64. [10] N. Roberston and P.D. Seymour, Graph minors II: algorithmic aspects of tree width, J. of Algorithms, 7 (1986), 309-322. [11] D.J. Rose, On simple characterizations of k-trees, Discrete Math., 7 (1974), 317-322. [12] J.R. Walter, Representations of chordal graphs as subtrees of a tree, J. Graph Theory, 2 (1978), 265-267. 描述 碩士
國立政治大學
應用數學系數學教學碩士在職專班
98972004資料來源 http://thesis.lib.nccu.edu.tw/record/#G0098972004 資料類型 thesis dc.contributor.advisor 張宜武 zh_TW dc.contributor.author (Authors) 游朝凱 zh_TW dc.creator (作者) 游朝凱 zh_TW dc.date (日期) 2011 en_US dc.date.accessioned 10-May-2016 19:33:38 (UTC+8) - dc.date.available 10-May-2016 19:33:38 (UTC+8) - dc.date.issued (上傳時間) 10-May-2016 19:33:38 (UTC+8) - dc.identifier (Other Identifiers) G0098972004 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/96375 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 應用數學系數學教學碩士在職專班 zh_TW dc.description (描述) 98972004 zh_TW dc.description.abstract (摘要) 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。 zh_TW dc.description.abstract (摘要) The chordality of a graph G = (V;E) is dened 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 dened 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. en_US dc.description.abstract (摘要) 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 - dc.description.tableofcontents Abstract ii 中文摘要iii 1 Introduction 1 1.1 History of Chordality and Treewidth 1 1.2 The Denition 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 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0098972004 en_US dc.subject (關鍵詞) 和弦圖數 zh_TW dc.subject (關鍵詞) 樹寬 zh_TW dc.subject (關鍵詞) 樹分解 zh_TW dc.subject (關鍵詞) 系列平行圖 zh_TW dc.subject (關鍵詞) Chordality en_US dc.subject (關鍵詞) Treewidth en_US dc.subject (關鍵詞) Tree Decomposition en_US dc.subject (關鍵詞) Series Parallel Graph en_US dc.title (題名) 圖之和弦圖數與樹寬 zh_TW dc.title (題名) The Chordality and Treewidth of a Graph en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] L.W. Beineke and R.E. Pippert, Properties and characterizations of k-trees, Mathematika, 18 (1971), 141-151. [2] P. Bumeman, A characterization of rigid circuit graphs, Discrete Mathematics, 9 (1974), 205-212. [3] M.B. Cozzens and F.S. Roberts, On dimensional properties of graphs, Graphs and Combinatorics, 5 (1989), 29-46. [4] G.A. Dirac, A property of 4-chromatic graphs and some remarks on critical graphs, J. London Math. Soc., 27 (1952), 85-92. [5] R.J. Dun, Topology of series parallel-networks, J. Math. Anal. Appl., 10 (1965), 303-318. [6] F. Gavril, The intersection graphs of subtrees in trees are exactly the chordal graphs, Journal of Combinatorial Theory (B), 16 (1974), 47-56. [7] Pinar Heggernes, Treewidth, partial k-trees, and chordal graphs, Delpensum INF 334- Institutt for informatikk, (2006). [8] Terry A. McKee and Edward R. Sceinerman, On the Chordality of a Graph, Journal of Graph Theory, 17 (1993), 221-232. [9] H.P. Patil, On the structure of k{trees, J. Combin. Inform. System. Sci., 11 (1986), 57-64. [10] N. Roberston and P.D. Seymour, Graph minors II: algorithmic aspects of tree width, J. of Algorithms, 7 (1986), 309-322. [11] D.J. Rose, On simple characterizations of k-trees, Discrete Math., 7 (1974), 317-322. [12] J.R. Walter, Representations of chordal graphs as subtrees of a tree, J. Graph Theory, 2 (1978), 265-267. zh_TW
