政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/94850

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/94850

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政大機構典藏 > 理學院 > 應用數學系 > 學位論文 > Item 140.119/94850

請使用永久網址來引用或連結此文件: https://nccur.lib.nccu.edu.tw/handle/140.119/94850

題名:	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
貢獻者:	張宜武郭瓊雲
關鍵詞:	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
上傳時間:	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
資料類型:	thesis
顯示於類別:	[應用數學系] 學位論文

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