On the validity of the core-mass luminosity relation for TP-AGB stars withefficient dredge-up

We investigate the validity of the core mass - luminosity relation (CMLR), originally described by Paczyriski (1970), for asymptotic giant branch star s under the presence of third dredge-up events. We find, that models with e fficient third dredge-up with less massive cores than those associated with hot bottom burning (Blocker and Schonberner, 1991) do not obey the linear CMLR. Complete evolutionary calculations of thermal pulse stellar models which co nsider overshoot according to an exponential diffusive algorithm show syste matically larger third dredge-up for lower core masses (0.55M. less than or similar to M-H less than or equal to 0.8M.) than any other existing models . We present and discuss the luminosity evolution of these models.