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題名 有關有弦探測圖形的探討
Some Problems on Chordal Probe Graphs
作者 李則旻
Lee, Tse Min
貢獻者 張宜武
李則旻
Lee, Tse Min
關鍵詞 有弦圖形
有弦深測圖形
Chordal Graphs
Chordal Probe Graphs
日期 2012
上傳時間 1-Feb-2013 16:53:17 (UTC+8)
摘要 在這篇論文中，我們探討有弦探測圖形與三方星狀圖、完美有序圖、
     排列圖的關係。另外我們給一些有弦探測圖形的例子並找到一個有弦
     探測圖形的必要的條件。最後我們探討一些有關有弦探測圖與其他圖
     的包含關係。
1 Introduction 1
     2 Some definitions and examples of graphs 4
     2.1 Interval graphs and Interval probe graphs . . . . . . . . . . . . . . 4
     2.2 Chordal graphs, Chordal probe graphs, and Weakly chordal graphs 6
     2.3 Asteroidal triple graphs (AT graphs) . . . . . . . . . . . . . . . . . 7
     2.4 Transitive orientations and Comparability graphs . . . . . . . . . . 7
     2.5 Alternately orientable graphs . . . . . . . . . . . . . . . . . . . . . 8
     2.6 Perfectly orderable graphs . . . . . . . . . . . . . . . . . . . . . . . 9
     2.7 Permutation graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
     2.8 Perfect graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
     2.9 2+2+2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
     3 Chordal probe graphs and other classes of graphs 12
     3.1 Chordal probe graphs and asteroidal triple graphs . . . . . . . . . . 12
     3.2 Chordal probe graphs and perfectly orderable graphs . . . . . . . . 16
     3.3 Chordal probe graphs and permutation graphs . . . . . . . . . . . . 20
     3.4 Some examples of chordal probe graphs and a necessary condition of
     being a chordal probe graph . . . . . . . . . . . . . . . . . . . . . 24
     4 Other classes of graphs containing the class of chordal probe graphs 28
     4.1 Hierarchy of classes of chordal probe graphs . . . . . . . . . . . . . 28
     4.2 Some containment relationships between chordal probe graphs and
     other classes of graphs . . . . . . . . . . . . . . . . . . . . . . . . . 29
     5 Open Problems and Further Directions of Studies 32
     Bibliography 33
參考文獻 [1] J. P. S. Andreas Brandstädt, Van Bang Le, Graph classes: A survey,
     SIAM Monographs on Discrete Math. and Applications, (1999).
     [2] C. Berge and e. Chvatal, Topics on perfect graphs, Annals of discrete
     mathematics, 21 (1984).
     [3] M. C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic
     Press, 1980.
     [4] R. B. Hayward, Weakly triangulated graphs, Journal of Combinatorial Theory,
     Series B, 39 (1985), pp. 200–208.
     [5] C. G. Lekkerkerker and J. C. Boland, Representation of a finite graph
     by a set of intervals on the real line, Fundamenta Mathematicae, 51 (1962),
     pp. 45–64.
     [6] L. L. M. Grotschel and A. Schrijver, The ellipsoid method and its consequences
     in combinatorial optimization, Combinatorica, 1 (1981), pp. 169–197.
     [7] A. N. T. Martin Charles Golumbic, Tolerance Graphs, Cambridge University
     Press, 2004.
     [8] M. L. Martin Charles Golumbic, Chordal probe graphs, Discrete Applied
     Mathematics, 143 (2004), pp. 221–237.
     [9] L. L. J. J. R. Peisen Zhang, Xiaolu Ye and S. G. Fischer, Integrated
     mapping package, Genomics, 55 (1999), pp. 78–87.
     [10] D. B. West, Introduction to Graph Theory, Prentice Hall, 2001.
     33
描述 碩士
國立政治大學
應用數學研究所
99751001
101
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0099751001
資料類型 thesis
dc.contributor.advisor 張宜武zh_TW
dc.contributor.author (Authors) 李則旻zh_TW
dc.contributor.author (Authors) Lee, Tse Minen_US
dc.creator (作者) 李則旻zh_TW
dc.creator (作者) Lee, Tse Minen_US
dc.date (日期) 2012en_US
dc.date.accessioned 1-Feb-2013 16:53:17 (UTC+8)-
dc.date.available 1-Feb-2013 16:53:17 (UTC+8)-
dc.date.issued (上傳時間) 1-Feb-2013 16:53:17 (UTC+8)-
dc.identifier (Other Identifiers) G0099751001en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/56879-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學研究所zh_TW
dc.description (描述) 99751001zh_TW
dc.description (描述) 101zh_TW
dc.description.abstract (摘要) 在這篇論文中，我們探討有弦探測圖形與三方星狀圖、完美有序圖、
     排列圖的關係。另外我們給一些有弦探測圖形的例子並找到一個有弦
     探測圖形的必要的條件。最後我們探討一些有關有弦探測圖與其他圖
     的包含關係。		zh_TW
dc.description.abstract (摘要) 1 Introduction 1
     2 Some definitions and examples of graphs 4
     2.1 Interval graphs and Interval probe graphs . . . . . . . . . . . . . . 4
     2.2 Chordal graphs, Chordal probe graphs, and Weakly chordal graphs 6
     2.3 Asteroidal triple graphs (AT graphs) . . . . . . . . . . . . . . . . . 7
     2.4 Transitive orientations and Comparability graphs . . . . . . . . . . 7
     2.5 Alternately orientable graphs . . . . . . . . . . . . . . . . . . . . . 8
     2.6 Perfectly orderable graphs . . . . . . . . . . . . . . . . . . . . . . . 9
     2.7 Permutation graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
     2.8 Perfect graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
     2.9 2+2+2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
     3 Chordal probe graphs and other classes of graphs 12
     3.1 Chordal probe graphs and asteroidal triple graphs . . . . . . . . . . 12
     3.2 Chordal probe graphs and perfectly orderable graphs . . . . . . . . 16
     3.3 Chordal probe graphs and permutation graphs . . . . . . . . . . . . 20
     3.4 Some examples of chordal probe graphs and a necessary condition of
     being a chordal probe graph . . . . . . . . . . . . . . . . . . . . . 24
     4 Other classes of graphs containing the class of chordal probe graphs 28
     4.1 Hierarchy of classes of chordal probe graphs . . . . . . . . . . . . . 28
     4.2 Some containment relationships between chordal probe graphs and
     other classes of graphs . . . . . . . . . . . . . . . . . . . . . . . . . 29
     5 Open Problems and Further Directions of Studies 32
     Bibliography 33		-
dc.description.tableofcontents 1 Introduction 1
     2 Some definitions and examples of graphs 4
     2.1 Interval graphs and Interval probe graphs . . . . . . . . . . . . . . 4
     2.2 Chordal graphs, Chordal probe graphs, and Weakly chordal graphs 6
     2.3 Asteroidal triple graphs (AT graphs) . . . . . . . . . . . . . . . . . 7
     2.4 Transitive orientations and Comparability graphs . . . . . . . . . . 7
     2.5 Alternately orientable graphs . . . . . . . . . . . . . . . . . . . . . 8
     2.6 Perfectly orderable graphs . . . . . . . . . . . . . . . . . . . . . . . 9
     2.7 Permutation graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
     2.8 Perfect graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
     2.9 2+2+2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
     3 Chordal probe graphs and other classes of graphs 12
     3.1 Chordal probe graphs and asteroidal triple graphs . . . . . . . . . . 12
     3.2 Chordal probe graphs and perfectly orderable graphs . . . . . . . . 16
     3.3 Chordal probe graphs and permutation graphs . . . . . . . . . . . . 20
     3.4 Some examples of chordal probe graphs and a necessary condition of
     being a chordal probe graph . . . . . . . . . . . . . . . . . . . . . 24
     4 Other classes of graphs containing the class of chordal probe graphs 28
     4.1 Hierarchy of classes of chordal probe graphs . . . . . . . . . . . . . 28
     4.2 Some containment relationships between chordal probe graphs and
     other classes of graphs . . . . . . . . . . . . . . . . . . . . . . . . . 29
     5 Open Problems and Further Directions of Studies 32
     Bibliography 33		zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0099751001en_US
dc.subject (關鍵詞) 有弦圖形zh_TW
dc.subject (關鍵詞) 有弦深測圖形zh_TW
dc.subject (關鍵詞) Chordal Graphsen_US
dc.subject (關鍵詞) Chordal Probe Graphsen_US
dc.title (題名) 有關有弦探測圖形的探討zh_TW
dc.title (題名) Some Problems on Chordal Probe Graphsen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] J. P. S. Andreas Brandstädt, Van Bang Le, Graph classes: A survey,
     SIAM Monographs on Discrete Math. and Applications, (1999).
     [2] C. Berge and e. Chvatal, Topics on perfect graphs, Annals of discrete
     mathematics, 21 (1984).
     [3] M. C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic
     Press, 1980.
     [4] R. B. Hayward, Weakly triangulated graphs, Journal of Combinatorial Theory,
     Series B, 39 (1985), pp. 200–208.
     [5] C. G. Lekkerkerker and J. C. Boland, Representation of a finite graph
     by a set of intervals on the real line, Fundamenta Mathematicae, 51 (1962),
     pp. 45–64.
     [6] L. L. M. Grotschel and A. Schrijver, The ellipsoid method and its consequences
     in combinatorial optimization, Combinatorica, 1 (1981), pp. 169–197.
     [7] A. N. T. Martin Charles Golumbic, Tolerance Graphs, Cambridge University
     Press, 2004.
     [8] M. L. Martin Charles Golumbic, Chordal probe graphs, Discrete Applied
     Mathematics, 143 (2004), pp. 221–237.
     [9] L. L. J. J. R. Peisen Zhang, Xiaolu Ye and S. G. Fischer, Integrated
     mapping package, Genomics, 55 (1999), pp. 78–87.
     [10] D. B. West, Introduction to Graph Theory, Prentice Hall, 2001.
     33		zh_TW