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arXiv · 1907.13292

The character graph of a finite group is perfect

Mahdi Ebrahimi
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Abstract

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

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Mahdi Ebrahimi. 2019-07-30. The character graph of a finite group is perfect. https://doi.org/10.1017/s0004972720001240

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