Exactly. Harmonic progression is probably the most important part of this, as it imparts context on the melody. The same melody over I-V-IV-vi and vi-V-IV-V is not the same thing.
And apparently arpeggios, because the US District Court of California ruled in Flame vs Katy Perry that arpeggios are "melodic enough" for copyright protection.
A combination of chords, melody, rhythm are I think the only reasonable measure that a song has been copied.
If I take the entire melody of a Beatles song, including the verse and chorus, but set it to an entirely different chord progression, would the court recognize that as an original song? What if I lifted all of the lyrics as well?