For a finite group G, let $\Delta (G)$ denote the character graph built on the set of degrees of the irreducible complex characters of G. A perfect graph is a graph $\Gamma $ in which the chromatic number of every induced subgraph $\Delta $ of $\Gamma $ equals the clique number of $\Delta $ . We show that the character graph $\Delta (G)$ of a finite group G is always a perfect graph. We also prove that the chromatic number of the complement of $\Delta (G)$ is at most three.

中文翻译：

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有限群的特征图是完美的

对于有限群G， 让 $\三角洲（G）$ 表示建立在不可约复特征的度集上的特征图G. 完美图是一个图 $\伽马$ 其中每个诱导子图的色数 $\三角洲$ 的 $\伽马$ 等于集团数 $\三角洲$ . 我们证明了字符图 $\三角洲（G）$ 有限群的G总是一个完美的图形。我们还证明了补码的色数 $\三角洲（G）$ 最多三个。