The -property of some classes of graphs

In this note, the 〈 t 〉 -properties of five classes of graphs are studied. We prove that the classes of cographs and clique perfect graphs without isolated vertices satisfy the 〈2〉-property and the 〈3〉-property, but do not satisfy the 〈 t 〉 -property for t ≥ 4 . The 〈 t 〉 -properties of the planar graphs and the perfect graphs are also studied. We obtain a necessary and sufficient condition for the trestled graph of index k to satisfy the 〈2〉-property.