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    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

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