In this paper, we characterize the class of {\em contraction perfect} graphs which are the graphs that remain perfect after the contraction of any edge set. We prove that a graph is contraction perfect if and only if it is perfect and the contraction of any single edge preserves its perfection. This yields a characterization of contraction perfect graphs in terms of forbidden induced subgraphs, and a polynomial algorithm to recognize them. We also define the utter graph $u(G)$ which is the graph whose stable sets are in bijection with the co-2-plexes of $G$, and prove that $u(G)$ is perfect if and only if $G$ is contraction perfect.

翻译：本文刻画了完美图经过任意边集收缩后仍保持完美性的图类——即完美收缩图。我们证明一个图是完美收缩图当且仅当它本身是完美图且任意单条边的收缩均能保持其完美性。这一结果给出了完美收缩图关于禁止诱导子图的结构特征，并提出了多项式时间识别算法。同时定义$u(G)$为稳定集与$G$的余2-团呈双射关系的完全图，证明$u(G)$是完美图当且仅当$G$是完美收缩图。