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Please use this identifier to cite or link to this item: https://ah.lib.nccu.edu.tw/handle/140.119/99611
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dc.contributor.advisor張宜武zh_TW
dc.contributor.author卓駿焰zh_TW
dc.creator卓駿焰zh_TW
dc.date2016en_US
dc.date.accessioned2016-08-03T02:14:26Zen_US
dc.date.copyright2016-08-03T02:14:26Zen_US
dc.date.created2016-08-03T02:14:26Zen_US
dc.identifierG0102751001en_US
dc.description碩士zh_TW
dc.description國立政治大學zh_TW
dc.description應用數學系zh_TW
dc.description102751001zh_TW
dc.description.abstract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。\r\n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 \r\n中文摘要 ii\r\nAbstract iii \r\nContents iv \r\nList of Figures vi\r\n1 Introduction 1\r\n2 (2,2)-Monochromatic-rectangles in a Checkerboard 3\r\n2.1 The Case of 2×n Checkerboard 4\r\n2.2 The Case of 3×n Checkerboard 5\r\n2.3 The Case of 4×n Checkerboard 6\r\n2.4 The Case of 5×n Checkerboard 7\r\n2.5 Summary 9\r\n3 (2,t)-monochromatic-rectangles in a Checkerboard 13\r\n3.1 The Case of 2×n Checkerboard 13 \r\n3.2 The Case of 3×n Checkerboard 13 \r\n3.3 The Case of 4×n Checkerboard 14\r\n3.4 The Case of 5×n Checkerboard 14 \r\n3.5 Summary 23\r\n4 (3,2)-Monochromatic-rectangles in a Checkerboard 24\r\n4.1 The Case of 3×n Checkerboard 24 \r\n4.2 The Case of 4×n Checkerboard 24 \r\n4.3 The Case of 5×n Checkerboard 24 \r\n4.4 The Case of 6×n Checkerboard 25 \r\n4.5 Summary 26\r\n5 (3,t)-Monochromatic-rectangles in a Checkerboard 27\r\n5.1 The Case of 5×n Checkerboard 27 \r\n5.2 The Case of 6×n Checkerboard 28 \r\n5.3 Summary 28\r\n6 (s,2)-Monochromatic-rectangles in a Checkerboard 29\r\n6.1 The Case of (2s−2)×n Checkerboard 29 \r\n6.2 The Case of (2s−1)×n Checkerboard 29 \r\n6.3 The Case of 2s×nCheckerboard 30 \r\n6.4 Summary 31\r\n7 (s,t)-Monochromatic-rectangles in a Checkerboard 32\r\n7.1 The Case of (2s−1)×n Checkerboard 32 \r\n7.2 The Case of 2s×n Checkerboard 33 \r\n7.3 Summary 33\r\nBibliography 34zh_TW
dc.source.urihttp://thesis.lib.nccu.edu.tw/record/#G0102751001en_US
dc.subject完全二分圖zh_TW
dc.subject單色子圖zh_TW
dc.titleThe Existence of (s,t)-Monochromatic-rectangles in a 2-colored Checkerboardzh_TW
dc.typethesisen_US
dc.relation.reference[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.\r\n[2] Douglas B. West. Introduction to graph theory. Prentice Hall, Inc., Upper Saddle River, NJ, 1996.\r\n[3] 李炯生. 棋盤染色問題與二部 Ramsey 數. 數學, 21(3):63–72, 9 月 1997.\r\n[4] 林子軒. The coloring of a checkerboard and the monochromatic subgraphs of a complete bipartite graph. 國立政治大學應用數學系碩士學位論文, 2013.zh_TW
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