政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/94850
English  |  正體中文  |  简体中文  |  Post-Print筆數 : 27 |  全文笔数/总笔数 : 113318/144297 (79%)
造访人次 : 51063559      在线人数 : 937
RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
搜寻范围 查询小技巧：
  • 您可在西文检索词汇前后加上"双引号"，以获取较精准的检索结果
  • 若欲以作者姓名搜寻，建议至进阶搜寻限定作者字段，可获得较完整数据
    •  进阶搜寻
    政大機構典藏 > 理學院 > 應用數學系 > 學位論文 >  Item 140.119/94850


    请使用永久网址来引用或连结此文件: https://nccur.lib.nccu.edu.tw/handle/140.119/94850


    题名: 最大外平面圖的有界容忍表示法
    Bounded Tolerance Representation for Maximal Outerplanar Graphs
    作者: 郭瓊雲
    贡献者: 張宜武
    郭瓊雲
    关键词: 最大外平面圖
    有界容忍表示法
    區間圖
    Tolerance graphs
    Maximal outerplanar graphs
    Interval graphs
    日期: 2008
    上传时间: 2016-05-09 11:58:27 (UTC+8)
    摘要: 本文針對2-連通的最大外平面圖，討論其有界容忍表示法，且找到禁止子圖S3。我們更進一步證明：如果一個2-連通的最大外平面圖恰有兩個點的度為2時，則此圖為區間圖。
    We prove that a 2-connected maximal outerplanar graph G is a bounded tolerance graph if and only if there is no induced subgraph S3 of G and G has no
    induced subgraph S3 if and only if G is an interval graph.
    Contents
    Abstract i
    中文摘要 ii
    1 Introduction 1
    1.1 History of tolerance graphs ...........................1
    1.2 The structure of tolerance graphs......................3
    2 Tolerance graphs 4
    2.1 Definition and theorems of tolerance graphs............4
    2.2 Bounded tolerance representations for trees and bipartite graphs ..........................................8
    3 Some results on maximal outerplanar graphs 10
    3.1 A 2-connected maximal outerplanar graph is not necessarily a tolerance graph.............................10
    3.2 Bounded tolerance representations for 2-connected maximal outerplanar graphs................................15
    4 Open problems and further directions of study 22
    References 23
    參考文獻: [1] K. Bogart, P. Fishburn, G. Isaak, and L. Langley, 1995. Proper and unit tolerance
    graphs. Discrete Applied Math., 60 37-51.
    [2] S. Felsner, 1998. Tolerance graphs and orders. J. Graph Theory, 28 129{140.
    [3] S. Fisher, R. MÄuller, and L. Wernisch, 1997. Trapezoid graphs and generaliza-
    tions, geometry and algorithms. Discrete Applied Math., 74 13-32.
    [4] M. C. Golumbic, 1980. Algorithmic Graph Theory and Perfect graphs. Academic
    Press.
    [5] M. C. Golumbic and C. L. Monma, 1982. A generalization of interval graphs
    with tolerances. Congress. Numer., 15 321-331.
    [6] M. C. Golumbic, C. L. Monma, and W. T. Trotter, 1984. Tolerance graphs.
    Discrete Applied Math., 9 157-170.
    [7] M. C. Golumbic and A. N. Trenk, 2004. Tolerance graphs, Cambridge University
    Press. Cambridge.
    [8] M. C. Golumbic, D. Rotem, and J. Urrutia, 1983. Comparability graphs and
    intersection graphs. Discrete Math., 43 37-46.
    [9] R. B. Hayward and R. Shamir, 2002. A note on tolerance graph recognition.
    Discrete Applied Math.
    [10] M. S. Jacobsen, F. R. McMorris and E. R. Scheinerman, General results on
    tolerance intersection graphs. J. Graph Theory, 15 573-578.
    [11] L. Langley, 1993. Interval tolerance orders and dimension. Ph. D. thesis, Dart-
    mouth College.
    描述: 碩士
    國立政治大學
    應用數學系
    95751006
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0095751006
    数据类型: thesis
    显示于类别:[應用數學系] 學位論文

    文件中的档案:

    档案 大小格式浏览次数
    index.html0KbHTML2203检视/开启


    在政大典藏中所有的数据项都受到原著作权保护.


    社群 sharing

    著作權政策宣告 Copyright Announcement
    1.本網站之數位內容為國立政治大學所收錄之機構典藏，無償提供學術研究與公眾教育等公益性使用，惟仍請適度，合理使用本網站之內容，以尊重著作權人之權益。商業上之利用，則請先取得著作權人之授權。
    The digital content of this website is part of National Chengchi University Institutional Repository. It provides free access to academic research and public education for non-commercial use. Please utilize it in a proper and reasonable manner and respect the rights of copyright owners. For commercial use, please obtain authorization from the copyright owner in advance.

    2.本網站之製作，已盡力防止侵害著作權人之權益，如仍發現本網站之數位內容有侵害著作權人權益情事者，請權利人通知本網站維護人員(nccur@nccu.edu.tw)，維護人員將立即採取移除該數位著作等補救措施。
    NCCU Institutional Repository is made to protect the interests of copyright owners. If you believe that any material on the website infringes copyright, please contact our staff(nccur@nccu.edu.tw). We will remove the work from the repository and investigate your claim.
    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library IR team Copyright ©   - 回馈