Chromatic choosability for some classes of perfect graphs

A graph Formula: see text is called Formula: see text-list colorable if there is a vertex coloring of Formula: see text in which the color assigned to a vertex Formula: see text is chosen from a list Formula: see text associated with this vertex. We say Formula: see text is Formula: see text-choosable if all lists Formula: see text have the cardinality Formula: see text and Formula: see text is Formula: see text-list colorable for all possible assignments of such lists. A graph Formula: see text is said to be chromatic choosable if its chromatic and list chromatic numbers are equal. Investigation of Formula: see text-choosable graphs is one of the open problems. In this paper, we investigate this problem for classes of perfect graphs.