Reading the definitions of T Tauri stars and the Hayashi track one can gather that:
T Tauri stars are pre-main-sequence stars in the process of contracting to the main sequence along the Hayashi track
and that:
After a protostar ends its phase of rapid contraction and becomes a T Tauri star, it is extremely luminous. The star continues to contract, but much more slowly. While slowly contracting, the star follows the Hayashi track
Can we then say that all stars on the Hayashi track are T Tauri stars? And moreover, are all T Tauris on the Hayashi track?