請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/57902完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 張鎮華(Gerard Jennhwa Chang) | |
| dc.contributor.author | Ting-Feng Jian | en |
| dc.contributor.author | 簡廷豐 | zh_TW |
| dc.date.accessioned | 2021-06-16T07:10:35Z | - |
| dc.date.available | 2014-08-01 | |
| dc.date.copyright | 2014-07-15 | |
| dc.date.issued | 2014 | |
| dc.date.submitted | 2014-07-07 | |
| dc.identifier.citation | [1] Michał Karoński, Tomasz Łuczak, and Andrew Thomason, Edge weights and vertex colours, Journal of Combinatorial Theory, Series B 91 (2004), 151-157.
[2] Tomasz Bartnicki, Jarosław Grytczuk, and Stanisław Niwczyk1, Weight choosability of graphs, Journal of Graph Theory 60 (2009), 242–256. [3] Noga Alon, Combinatorial Nullstellensatz, Combinatorics Probability and Computing 8 (1999), 7-29. [4] Louigi Addario-Berry, Ketan Dalal, Colin McDiarmid, Bruce A. Reed, and Andrew Thomason, Vertex-colouring edge-weightings, Combinatorica 27 (2007), 1-12. [5] Louigi Addario-Berry, Ketan Dalal, and Bruce A. Reed , Degree constrainted subgraphs, Discrete Applied Mathematics 156 (2008), 1168-1174. [6] Tao Wang and Qinglin Yu, On vertex-coloring 13-edge-weighting, Frontiers of Mathematics in China 3 (2008), 1-7. [7] Maciej Kalkowski, Michał Karoński, and Florian Pfender, Vertex-coloring edge-weightings with integer weights at most 6, Rostocker Mathematisches Kolloquium 64 (2009), 39-44. [8] Maciej Kalkowski, Michał Karoński, and Florian Pfender, Vertex-coloring edge-weighting: towards the 1-2-3-Conjecture, Journal of Combinatorial Theory, Series B 100 (2010), 347-349. [9] Tsai-Lien Wong and Xuding Zhu, Total weight choosability of graphs, Journal of Graph Theory, submitted. [10] Maciej Kalkowski, Michał Karoński, and Florian Pfender, The 1-2-3 conjecture for hypergraphs, submitted. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/57902 | - |
| dc.description.abstract | 1, 2, 3猜想是由 M. Karoński等人於2004年所提出的邊權重點著色問題，
該問題由 T. Bartnicki等人於2009年推演成邊權重選擇性的問題。 儘管已經解決一些特殊的例子，這兩個問題現今仍尚未解決，也發展一些方法值得討論。 本文運用組合零點定理與積和式， 從環、theta圖與廣義theta圖著手發現一些結果。 其中最主要證明了這些圖皆為3-邊權重可選擇的。 | zh_TW |
| dc.description.abstract | The 1,2,3-conjecture is a problem of edge weight colorability of graphs which was posed by M. Karoński et al in 2004.
Further problem of edge weight choosability of graphs was posed by T. Bartnicki et al in 2009. While being solved for some special cases, the two problems are still open nowadays. In this thesis, we use the combinatorial nullstellensatz and the permanent to find some results. We go through the cycles, then discuss the θ-graphs and generalized θ-graphs. The main result of this thesis is to show these graphs are all 3-edge weight choosable. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T07:10:35Z (GMT). No. of bitstreams: 1 ntu-103-R01221001-1.pdf: 464160 bytes, checksum: 2dc5389adfbae474be2a4ae86a9f45b8 (MD5) Previous issue date: 2014 | en |
| dc.description.tableofcontents | Acknowledgements. . . . . . . . . . . . . . . . . i
Abstract (in Chinese) . . . . . . . . . . . . . . ii Abstract (in English) . . . . . . . . . . . . . . iii Contents. . . . . . . . . . . . . . . . . . . . . iv List of Figures . . . . . . . . . . . . . . . . . v 1. Introduction . . . . . . . . . . . . . . . . . 1 2. The Paths . . . . . . . . . . . . . . . . . . 8 3. The Cycles . . . . . . . . . . . . . . . . . . 11 4. The θ-graphs . . . . . . . . . . . . . . . . . 17 5. The Generalized θ-graphs . . . . . . . . . . . 29 6. Further Problems . . . . . . . . . . . . . . . 34 References. . . . . . . . . . . . . . . . . . . . 35 | |
| dc.language.iso | en | |
| dc.title | theta圖的權重選擇性 | zh_TW |
| dc.title | Weight Choosability of theta Graphs | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 102-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 顏經和(Jing-Ho Yan),葉鴻國(Hong-Gwa Yeh) | |
| dc.subject.keyword | 權重選擇性,3-權重可選的,組合零點定理,積和式,環,theta圖,廣義theta圖, | zh_TW |
| dc.subject.keyword | weight choosability,3-weight choosable,combinatorial nullstellensatz,permanent,cycles,θ-graphs,generalized θ-graphs, | en |
| dc.relation.page | 35 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2014-07-08 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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