Using Git, show all commits that exist *only* on one specific branch, and not *any* others

We just found this elegant solution

git log --first-parent --no-merges

In your example of course the initial commit still shows up.

this answer does not exactly answer the question, because the initial commit still shows up. On the other hand many people coming here seem to find the answer they are looking for.

Courtesy of my dear friend Redmumba:

git log --no-merges origin/merge-only \
    --not $(git for-each-ref --format="%(refname)" refs/remotes/origin |
    grep -Fv refs/remotes/origin/merge-only)

...where origin/merge-only is your remote merge-only branch name. If working on a local-only git repo, substitute refs/remotes/origin with refs/heads, and substitute remote branch name origin/merge-only with local branch name merge-only, i.e.:

git log --no-merges merge-only \
    --not $(git for-each-ref --format="%(refname)" refs/heads |
    grep -Fv refs/heads/merge-only)