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。

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.

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