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博碩士論文 etd-0705104-163710 詳細資訊
Title page for etd-0705104-163710
論文名稱
Title
Kneser 圖的環色數
Circular chromatic number of Kneser Graphs
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
10
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
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
統計
Statistics
本論文已被瀏覽 5721 次,被下載 2384
The thesis/dissertation has been browsed 5721 times, has been downloaded 2384 times.
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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