What legacy was established after the holocaust for nations to deal with genocide?

There are likely two answers to this. We have to cover 2 situations. In 1948 the United Nations adopted a resolution that all members (at that time) agreed to. The resolution said that all perpetrators of a genocide were to be punished. That covered members of the United Nations, but genocides have been committed since world WWII by nations other than those belonging to the UN.

How are those cases being handled and how well is the UN resolution obeyed.

When you look this question up, many more countries have agreed with the resolution, but still disobeyed its intent. China being one. Believe it or not, the US was accused of being another. There were others like Rwanda that really were guilty of Genocide who agreed with the policy but were not among the original ratifiers.

c.) the country needed a stronger central government.