For a graph $G$, we denote by $α(G)$ the size of a maximum independent set and by $ω(G)$ the size of a maximum clique in $G$. Our paper lies on the edge of two lines of research, related to $α$ and $ω$, respectively. One of them studies $α$-variants of graph parameters, such as $α$-treewidth or $α$-degeneracy. The second line deals with graph classes where some parameters are bounded by a function of $ω(G)$. A famous example of this type is the family of $χ$-bounded classes, where the chromatic number $χ(G)$ is bounded by a function of $ω(G)$. A Ramsey-type argument implies that if the $α$-variant of a graph parameter $ρ$ is bounded by a constant in a class $\mathcal{G}$, then $ρ$ is bounded by a function of $ω$ in $\mathcal{G}$. If the reverse implication also holds, we say that $ρ$ is awesome. Otherwise, we say that $ρ$ is awful. In the present paper, we identify a number of awesome and awful graph parameters, derive some algorithmic applications of awesomeness, and propose a number of open problems related to these notions.

翻译：对于图$G$，我们用$α(G)$表示最大独立集的大小，用$ω(G)$表示最大团的大小。本文的研究处于两条研究路线的交叉点，分别与$α$和$ω$相关。其中一条路线研究图参数的$α$变体，例如$α$-树宽或$α$-退化度。第二条路线研究某些参数以$ω(G)$的函数为界的图类。此类的一个著名例子是$χ$-有界类族，其中色数$χ(G)$以$ω(G)$的函数为界。根据拉姆齐型论证可知，若图参数$ρ$的$α$变体在类$\mathcal{G}$中为常数有界，则$ρ$在$\mathcal{G}$中以$ω$的函数为界。若反向蕴含关系也成立，则称$ρ$是卓越的；否则称$ρ$是糟糕的。本文识别了若干卓越与糟糕的图参数，推导了卓越性的一些算法应用，并提出了与这些概念相关的若干开放问题。