1. NCCU Academic Hub
  2. Publications
  3. College of Science
  4. Theses
  5. Item

Publications-Theses

Article View/Open

Publication Export

Google ScholarTM

NCCU Library

Citation Infomation

Related Publications in TAIR

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-Feb-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.\n[2] L. A. Melnikov, Problem at the "Sixth Hungar. Colloq. on Combinatorics", Eger, 1981.\n[3] E. R. Scheinerman, "Intersection Classes and Multiple Intersection Parameters", Ph. D. thesis, Princetion Uni., 1984.\n[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.\n[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.\n[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.\n[7] P. Unger, On diagrams representing maps, J. London Math. Soc. 28 (1953), pp.336-342\n[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 (Authors) 劉淑慧zh_TW
dc.creator (作者) 劉淑慧zh_TW
dc.date (日期) 2012en_US
dc.date.accessioned 1-Feb-2013 16:53:21 (UTC+8)-
dc.date.available 1-Feb-2013 16:53:21 (UTC+8)-
dc.date.issued (上傳時間) 1-Feb-2013 16:53:21 (UTC+8)-
dc.identifier (Other Identifiers) G0099972007en_US
dc.identifier.uri (URI) https://ah.lib.nccu.edu.tw/item?item_id=64448-
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) 99972007zh_TW
dc.description (描述) 101zh_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 ...........................................1\n2 Strict 2-box representation.............................4\n2.1 Defitions and theprem of cyclically 4-edge-connected \n planar graphs and 4-connected planar triangulation....4\n graphs \n2.2 Planar graphs have strict a 2-box representations by at \n least two boxes.......................................8\n3 Some results on d-box representation...................10\n3.1 A strict 2-box representation for 4-connected planar \n triangulation graphs.................................10\n3.2 A strict 3-box representation for planar graphs......18\n4 Open problems and further directions on study..........23\nReference................................................24zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0099972007en_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 graphsen_US
dc.subject (關鍵詞) 4-connected planar triangulation graphen_US
dc.subject (關鍵詞) strict d-box representationen_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 Graphsen_US
dc.type (資料類型) thesisen
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.\n[2] L. A. Melnikov, Problem at the "Sixth Hungar. Colloq. on Combinatorics", Eger, 1981.\n[3] E. R. Scheinerman, "Intersection Classes and Multiple Intersection Parameters", Ph. D. thesis, Princetion Uni., 1984.\n[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.\n[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.\n[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.\n[7] P. Unger, On diagrams representing maps, J. London Math. Soc. 28 (1953), pp.336-342\n[8] C. Thomassen, "Interval representations of planar graphs, Journal of Combinatorial Theory, Series B, pp.9-20, 1986.zh_TW