| dc.contributor.advisor | 張宜武 | zh_TW |
| dc.contributor.author (Authors) | 卓駿焰 | zh_TW |
| dc.creator (作者) | 卓駿焰 | zh_TW |
| dc.date (日期) | 2016 | en_US |
| dc.date.accessioned | 3-Aug-2016 10:14:26 (UTC+8) | en_US |
| dc.date.copyright | 3-Aug-2016 10:14:26 (UTC+8) | en_US |
| dc.date.created | 3-Aug-2016 10:14:26 (UTC+8) | en_US |
| dc.identifier (Other Identifiers) | G0102751001 | en_US |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學系 | zh_TW |
| dc.description (描述) | 102751001 | zh_TW |
| dc.description.abstract (摘要) | 本文藉由矩形棋盤著色探討完全二分圖K_{m,n}由兩種顏色任意塗邊，使得此兩色著邊之完全二分圖$K_{m,n}$會包含單色子圖K_{s,2}、K_{s,3}與K_{s,t} （s大於或等於 2），我們將討論參數n與s之間滿必須滿足何種關係。 本文也將介紹處理棋盤著色問題的一般方法與技巧，以及透過棋盤如何將棋盤問題轉化為圖論問題，並且將它推廣。 | zh_TW |
| dc.description.tableofcontents | 口試委員會審定書 i 中文摘要 ii Abstract iii Contents iv List of Figures vi 1 Introduction 1 2 (2,2)-Monochromatic-rectangles in a Checkerboard 3 2.1 The Case of 2×n Checkerboard 4 2.2 The Case of 3×n Checkerboard 5 2.3 The Case of 4×n Checkerboard 6 2.4 The Case of 5×n Checkerboard 7 2.5 Summary 9 3 (2,t)-monochromatic-rectangles in a Checkerboard 13 3.1 The Case of 2×n Checkerboard 13 3.2 The Case of 3×n Checkerboard 13 3.3 The Case of 4×n Checkerboard 14 3.4 The Case of 5×n Checkerboard 14 3.5 Summary 23 4 (3,2)-Monochromatic-rectangles in a Checkerboard 24 4.1 The Case of 3×n Checkerboard 24 4.2 The Case of 4×n Checkerboard 24 4.3 The Case of 5×n Checkerboard 24 4.4 The Case of 6×n Checkerboard 25 4.5 Summary 26 5 (3,t)-Monochromatic-rectangles in a Checkerboard 27 5.1 The Case of 5×n Checkerboard 27 5.2 The Case of 6×n Checkerboard 28 5.3 Summary 28 6 (s,2)-Monochromatic-rectangles in a Checkerboard 29 6.1 The Case of (2s−2)×n Checkerboard 29 6.2 The Case of (2s−1)×n Checkerboard 29 6.3 The Case of 2s×nCheckerboard 30 6.4 Summary 31 7 (s,t)-Monochromatic-rectangles in a Checkerboard 32 7.1 The Case of (2s−1)×n Checkerboard 32 7.2 The Case of 2s×n Checkerboard 33 7.3 Summary 33 Bibliography 34 | zh_TW |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0102751001 | en_US |
| dc.subject (關鍵詞) | 完全二分圖 | zh_TW |
| dc.subject (關鍵詞) | 單色子圖 | zh_TW |
| dc.title (題名) | The Existence of (s,t)-Monochromatic-rectangles in a 2-colored Checkerboard | zh_TW |
| dc.type (資料類型) | thesis | en_US |
| dc.relation.reference (參考文獻) | [1] Ronald L. Graham, Bruce L. Rothschild, and Joel H. Spencer. Ramsey theory. Wiley Series in Discrete Mathematics and Optimization. John Wiley & Sons, Inc., Hoboken, NJ, 2013. [2] Douglas B. West. Introduction to graph theory. Prentice Hall, Inc., Upper Saddle River, NJ, 1996. [3] æç¯ç. æ£ç¤æè²åé¡èäºé¨ Ramsey æ¸. æ¸å¸, 21(3):63â72, 9 æ 1997. [4] æåè». The coloring of a checkerboard and the monochromatic subgraphs of a complete bipartite graph. åç«æ¿æ²»å¤§å¸æç¨æ¸å¸ç³»ç¢©å£«å¸ä½è«æ, 2013. | zh_TW |
