On imperfect critical graphs with incomplete critical component

In this paper, we present two assertions that are collectively equivalent to the strong conjecture about imperfect graphs [1]. The article is devoted to the study of one of the statements. The previously known structure of a critical graph containing an incomplete critical component is given [2]. In conclusion, two conditions are found, each of which is necessary and sufficient for a critical graph containing an incomplete component to be an odd cycle without diagonals or its complement.