The 〈t〉〈t〉-property of some classes of graphs

In this note, the 〈t〉〈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〉〈t〉-property for t≥4t≥4. The 〈t〉〈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 kk to satisfy the 〈2〉-property.