圖形環著色數的若干等價定義

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連冠翔(Kuan-Hsiang Lien) 查詢紙本館藏

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論文名稱

圖形環著色數的若干等價定義
(On Equivalent Definitions of the Circular Chromatic Number of a Graph)

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摘要(中)

本論文回顧並證明圖形環著色數的若干等價定義，並使用這些等價定義，對一些圖形環著色數的古典基本結果給出新的證明。

摘要(英)

This report is aimed to survey equivalent definitions of circular chromatic numbers of graphs and their applications. We describe how to use these equivalent definitions to give new proofs for several basic classical results of circular chromatic numbers.

關鍵字(中)

★ 圖形環

關鍵字(英)

論文目次

1 Introduction and Preliminaries 1
2 Equivalent Definitions of the Circular Chromatic Number 3
3 New proofs for some basic classical results 10
參考文獻 14

參考文獻

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[2] J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, American Elsevier, 1979.
[3] Wu-Hsiung Lin and Hong-Gwa Yeh, A note on circular colorings of edge-weighted digraphs, Taiwanese Journal of Mathematics, 15 (2011) 2159-2167.
[4] D. B. West, Introduction to Graph Theory, 2nd edition, Prentice Hall, 2001.
[5] Hong-Gwa Yeh and Xuding Zhu, Resource-sharing system scheduling and circular chromatic number, Theoretical Computer Science 332 (2005) 447-460.
[6] Hong-Gwa Yeh, A dynamic view of circular colorings, preprint, 2006. http://arxiv.org/abs/math/ 0604226
[7] Hong-Gwa Yeh, Class Notes for Graph Structure Theory, Fall 2016, National Central University, Taiwan.
[8] Hong-Gwa Yeh, A method to obtain lower bounds for circular chromatic number, Taiwanese Journal of Mathematics, 12 (2008) 997-1005.
[9] Hong-Gwa Yeh, A connection between circular colorings and periodic schedules, Discrete Ap- plied Mathematics, 157 (2009) 1663-1668.
[10] Xuding Zhu, Circular chromatic number: a survey, Discrete Math. 229 (2001) 371-410.
[11] Xuding Zhu, Circular colouring and orientation of graphs, J. Comb. Theory, Ser. B, 86 (2002) 109-113.
[12] Xuding Zhu, Recent developments in circular colouring of graphs, In M. Klazar, J. Kratochvil,
J. Matousek, R. Thomas, and P. Valtr, editors, Topics in Discrete Mathematics, pages 497-550, Springer, 2006.

指導教授

葉鴻國(Hong-Gwa Yeh)

審核日期

2017-7-14

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