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論文名稱 Title |
Kneser 圖的環色數 Circular chromatic number of Kneser Graphs |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
10 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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口試日期 Date of Exam |
2004-06-04 |
繳交日期 Date of Submission |
2004-07-05 |
關鍵字 Keywords |
環色數、著色 circular chromatic number, Kneser graph |
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統計 Statistics |
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中文摘要 |
本論文在討論 Kneser 圖的環色數。 假如 m 大於或等於 2n^{2}(n-1) ,則Kneser 圖KG(m,n) 的環色數會相等於它的著色數這是已經知道的。 尤其是當 m 大於或等於 36 時,假如 n 等於 3,則KG(m,3) 的環色數會與本身的著色數相等。 在本論文中我們藉由假如 m 大於或等於 24,則 chi_{c}(KG(m,3)) = chi(KG(m,3)) 這個證明來改善這個結果。 |
Abstract |
This thesis studies the circular chromatic number of Kneser graphs. It was known that if m is greater than 2n^{2}(n-1), then the Kneser graph KG(m,n) has its circular chromatic number equal its chromatic number . In particular, if n = 3, then KG(m,3) has its circular chromatic number equal its chromatic number when m is greater than 36. In this thesis, we improve this result by proving that if m is greaer than 24, then chi_c(KG(m,3)) = chi(KG(m,3)). |
目次 Table of Contents |
Contents 1 Introduction 1 2 Some preliminaries 3 3 The main result 6 |
參考文獻 References |
[1] M. Kneser,Aufgabe 300, Jber. Deutsch. Math.-Verein 58 (1955),27. [2] X. Zhu, Circular chromatic number: a survey, Discrete Mathematics, 229 (1-3) (2001), 371-410. [3] H.Hajiabolhassan and X. Zhu, Circular chromatic number of Kneser graphs, J.Combin. Theory, Ser.B , 88 (2003) , 229-303 [4] L.Lov´asz, Kneser’s conjecture, chromatic number, and homoyopy, J.Combin. Theory, Ser.A, 25 (1978) , 319-324. [5] A.Vince, Star chromatic number, J.Graph Theory, 12 (1988) , 551-559. [6] A. Johnson, F.C.Holroyd, and S.Stahl, Multichromatic numbers, star chromatic numbers and Kneser graphs, J.Graph Theory, 26 (1997) , 137- 145. [7] A.J.W. Hilton and E.C. Milner, Some intersection theorems for systems of finite sets, Quart. J. Math. Oxford(2), 18 (1967) , 369-384. |
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