A graph $G$ is called $g$-perfect if, for any induced subgraph $H$ of $G$, the game chromatic number of $H$ equals the clique number of $H$. A graph $G$ is called $g$-col-perfect if, for any induced subgraph $H$ of $G$, the game coloring number of $H$ equals the clique number of $H$. In this paper we characterize the classes of $g$-perfect resp. $g$-col-perfect graphs by a set of forbidden induced subgraphs and explicitly. Moreover, we study similar notions for variants of the game chromatic number, namely $B$-perfect and $[A,B]$-perfect graphs, and for several variants of the game coloring number, and characterize the classes of these graphs.
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机译：如果对于$ G $的任何诱导子图$ H $，游戏色数$ H $等于集团数$ H $，则将图形$ G $称为$ g $完美。如果对于任何$ G $的诱导子图$ H $，游戏着色数$ H $等于集团数$ H $，则图$ G $称为$ g $ -col-perfect。在本文中，我们描述了完美的$ g $的类。 $ g $ -col-perfect图由一组禁止的诱导子图组成，并且是显式的。此外，我们研究了游戏色度数变体（即$ B $完美图和$ [A，B] $完美图）以及游戏色数的多个变体的相似概念，并对这些图的类别进行了表征。
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