The clique graph K (G ) of G is the intersection graph of the family of maximal cliques of G . For a family $\mathcal{F}$ of graphs, the family of clique‐inverse graphs of $\mathcal{F}$, denoted by $K^{-1}\left(\mathcal{F}\right)$, is defined as $K^{-1}\left(\mathcal{F}\right)=\left\{H|K\left(H\right)\in \mathcal{F}\right\}$. Let ${\mathcal{F}}_p$ be the family of K _p ‐free graphs, that is, graphs with clique number at most p  − 1, for an integer constant p  ≥ 2. Deciding whether a graph H is a clique‐inverse graph of ${\mathcal{F}}_p$ can be done in polynomial time; in addition, for $p\in \left\{2,3,4\right\},K^{-1}\left({\mathcal{F}}_p\right)$ can be characterized by a finite family of forbidden induced subgraphs. In Protti and Szwarcfiter, the authors propose to extend such characterizations to higher values of p . Then a natural question arises: Is there a characterization of $K^{-1}\left({\mathcal{F}}_p\right)$ by means of a finite family of forbidden induced subgraphs, for any p  ≥ 2? In this note we give a positive answer to this question. We present upper bounds for the order, the clique number, and the stability number of every forbidden induced subgraph for $K^{-1}\left({\mathcal{F}}_p\right)$ in terms of p .

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关于有界数字的图的集团逆图

所述集团图K（ģ的）ģ是家庭的最大派系的交叉图形ģ。对于一个家庭$\mathcal{F}$图，是图的集团反图族 $\mathcal{F}$，表示为 ${ķ}^{-\mathrm{1个}}（\mathcal{F}）$，定义为 ${ķ}^{-\mathrm{1个}}（\mathcal{F}）=\left\{H|ķ（H）\in \mathcal{F}\right\}$。让${\mathcal{F}}_p$是家族ķ _p -free图，即，具有至多团数曲线p  - 1，为一个整数常量p  ≥2决定的图表是否ħ是的团逆曲线图${\mathcal{F}}_p$可以在多项式时间内完成；另外，对于$p\in \left\{2，3，4\right\}，{ķ}^{-\mathrm{1个}}（{\mathcal{F}}_p）$可以通过有限的禁止诱导子图族来表征。在Protti和Szwarcfiter中，作者建议将这些特征扩展到p的较高值。然后一个自然的问题出现了：${ķ}^{-\mathrm{1个}}（{\mathcal{F}}_p）$通过的手段有限家庭禁止诱导子图，对于任何p  ≥2？在本说明中，我们对这个问题给出了肯定的答案。我们给出了每个禁止的诱导子图的阶数，集团数和稳定性数的上限${ķ}^{-\mathrm{1个}}（{\mathcal{F}}_p）$以p表示。