Self-stabilization is a versatile approach to fault-tolerance since it permits a distributed system to recover from any transient fault that arbitrarily corrupts the contents of all memories in the system. Byzantine tolerance is an attractive feature of distributed systems that permits to cope with arbitrary malicious behaviors. We consider the well known problem of constructing a maximum metric tree in this context. Combining these two properties leads to some impossibility results. In this paper, we provide two necessary conditions to construct maximum metric tree in presence of transients and (permanent) Byzantine faults.