The character graph of a finite group is perfect
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.
math.GR↗