Which journals publish short notes in discrete mathematics?
There are various general journals that are focused on "short papers." There a seven pages paper would fit just fine.
Examples include, Proceedings of the AMS, Bulletin of the LMS, Archiv der Mathematik. For more you could read Which journals publish 1-page papers
Yet, as discussed there even most other journals do not have an actual lower bound on the length of the paper; of course the paper has to be sufficiently substantive.
Furthermore, it is not that rare for a discrete mathematics paper to be short. For most journal specialized in combinatorics and discrete mathematics a paper of that length should not be anything unusual (consult the instructions for authors though).
For an overview about discrete mathematics journals see for example Two questions about combinatorics journals or the respective answers on Top specialized journals
Electronic Notes in Discrete Mathematics only publishes short notes in discrete mathematics.
The Electronic Journal of Combinatorics Current issue (issue 3, 2015), has the first two listed articles with $7$ and $8$ pages, so I assume there is no page minimum requirement.