Type of usage

A woman files for divorce from husband for cheating.

Do these form complete sentences with a predicate? (Does it not require her husband) Or is her just a determiner that can be omitted.

David Earl Miller's path to Tennessee's electric chair.

(How would you describe this?) I assume it's a title but where does it stand grammatically outside of it's context. Just a phrase with a subject ?

Some titles stand-alone, but the way it's written feels like it want to continue along?

David Earl Miller's path to Tennesee's electric chair was mired in controversy.

As opposed to The History of the World.