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題名 探討平面圖的d維矩形表示法
A Study on Strict d-box Representations of Planar Graphs作者 劉淑慧 貢獻者 張宜武博士
劉淑慧關鍵詞 區間圖
四連通三角平面圖
嚴格d維矩形表示法
interval graphs
4-connected planar triangulation graph
strict d-box representation日期 2012 上傳時間 1-二月-2013 16:53:21 (UTC+8) 摘要 本文我們探討平面圖形的嚴格d維矩形表示法。我們證明了四連通三角平面圖有嚴格的二維矩形表示法，而且我們推廣到每一個平面圖都有嚴格的三維矩形表示法。我們的目標是希望能在平面圖矩形表示法的現今地位上，提供新的洞悉,並給未來學習者一個方向。
We study strict d-box representations of planar graphs. We prove that a 4-connected planar triangulation graph G has a strict 2-box representation. We extend this result to that every planar graph has a strict 3-box representation. Our goal is to provide some fresh insights into the current status of research in the area while suggesting directions for the future.參考文獻 [1] P. Duchet, Y. Hamidoune, M. Las Vergas, and H. Meyniel, Representing a planar graph by vertical lines joing different levels, Discrete Math. 46(1983), 221-332.[2] L. A. Melnikov, Problem at the "Sixth Hungar. Colloq. on Combinatorics", Eger, 1981.[3] E. R. Scheinerman, "Intersection Classes and Multiple Intersection Parameters", Ph. D. thesis, Princetion Uni., 1984.[4] E. R. Scheinerman and D. B. West, "The interval number of a planar graph: Three intervals suffice, J. Combin. Theory Ser. B 35 (1983), 224-239.[5] C. Thomassen, Plane representations of graphs, in "Progress in Graph Theory", (J. A. Bondy and U. S. Murty, Eds.), pp.43-69, Academic Press, Toronto, 1984.[6] W. T. Trotter, Graphs and partially ordered sets, in "Selected Topics in Graph Theory 2", (L. W. Beineke and R. J. Wilson, Eds.), pp.237-268, Academic Press, London, 1983.[7] P. Unger, On diagrams representing maps, J. London Math. Soc. 28 (1953), pp.336-342[8] C. Thomassen, "Interval representations of planar graphs, Journal of Combinatorial Theory, Series B, pp.9-20, 1986. 描述 碩士
國立政治大學
應用數學研究所
99972007
101資料來源 http://thesis.lib.nccu.edu.tw/record/#G0099972007 資料類型 thesis dc.contributor.advisor 張宜武博士 zh_TW dc.contributor.author (作者) 劉淑慧 zh_TW dc.creator (作者) 劉淑慧 zh_TW dc.date (日期) 2012 en_US dc.date.accessioned 1-二月-2013 16:53:21 (UTC+8) - dc.date.available 1-二月-2013 16:53:21 (UTC+8) - dc.date.issued (上傳時間) 1-二月-2013 16:53:21 (UTC+8) - dc.identifier (其他 識別碼) G0099972007 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/56883 - 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) 99972007 zh_TW dc.description (描述) 101 zh_TW dc.description.abstract (摘要) 本文我們探討平面圖形的嚴格d維矩形表示法。我們證明了四連通三角平面圖有嚴格的二維矩形表示法，而且我們推廣到每一個平面圖都有嚴格的三維矩形表示法。我們的目標是希望能在平面圖矩形表示法的現今地位上，提供新的洞悉,並給未來學習者一個方向。 zh_TW dc.description.abstract (摘要) We study strict d-box representations of planar graphs. We prove that a 4-connected planar triangulation graph G has a strict 2-box representation. We extend this result to that every planar graph has a strict 3-box representation. Our goal is to provide some fresh insights into the current status of research in the area while suggesting directions for the future. en_US dc.description.tableofcontents 1 Introduction ...........................................12 Strict 2-box representation.............................42.1 Defitions and theprem of cyclically 4-edge-connected planar graphs and 4-connected planar triangulation....4 graphs 2.2 Planar graphs have strict a 2-box representations by at least two boxes.......................................83 Some results on d-box representation...................103.1 A strict 2-box representation for 4-connected planar triangulation graphs.................................103.2 A strict 3-box representation for planar graphs......184 Open problems and further directions on study..........23Reference................................................24 zh_TW dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0099972007 en_US dc.subject (關鍵詞) 區間圖 zh_TW dc.subject (關鍵詞) 四連通三角平面圖 zh_TW dc.subject (關鍵詞) 嚴格d維矩形表示法 zh_TW dc.subject (關鍵詞) interval graphs en_US dc.subject (關鍵詞) 4-connected planar triangulation graph en_US dc.subject (關鍵詞) strict d-box representation en_US dc.title (題名) 探討平面圖的d維矩形表示法 zh_TW dc.title (題名) A Study on Strict d-box Representations of Planar Graphs en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) [1] P. Duchet, Y. Hamidoune, M. Las Vergas, and H. Meyniel, Representing a planar graph by vertical lines joing different levels, Discrete Math. 46(1983), 221-332.[2] L. A. Melnikov, Problem at the "Sixth Hungar. Colloq. on Combinatorics", Eger, 1981.[3] E. R. Scheinerman, "Intersection Classes and Multiple Intersection Parameters", Ph. D. thesis, Princetion Uni., 1984.[4] E. R. Scheinerman and D. B. West, "The interval number of a planar graph: Three intervals suffice, J. Combin. Theory Ser. B 35 (1983), 224-239.[5] C. Thomassen, Plane representations of graphs, in "Progress in Graph Theory", (J. A. Bondy and U. S. Murty, Eds.), pp.43-69, Academic Press, Toronto, 1984.[6] W. T. Trotter, Graphs and partially ordered sets, in "Selected Topics in Graph Theory 2", (L. W. Beineke and R. J. Wilson, Eds.), pp.237-268, Academic Press, London, 1983.[7] P. Unger, On diagrams representing maps, J. London Math. Soc. 28 (1953), pp.336-342[8] C. Thomassen, "Interval representations of planar graphs, Journal of Combinatorial Theory, Series B, pp.9-20, 1986. zh_TW
