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.