Does the father Tiger leave after the cubs are born?

Yes. Then he has no more duties as far as raising the cubs.

This is because the father believes the cubs may one day take control of his territory, which also is having his mates too. Then the father would be left with nothing. That's why father tigers sometimes will kill their offspring.

Luckily, tigresses will protect their cubs from their fathers. Most of the population is decreased by humans, not father tigers.

Actually, it is extremely rare for male tigers to kill their own young. Males sometimes will rejoin their family, and may even hunt with them for a time. Male tigers may kill cubs that are not their own, however.