Undergraduate prerequisites for a Ph.d. in combinatorics
The prerequisites in combinatorics will not be significantly different from the overall prerequisites in the program to which you are applying.  Having taken a combinatorics course would be beneficial, but there is no need to take many of them as an undergraduate.  You mention Budapest Semesters in Mathematics in a comment.  They offer a lot of combinatorics courses, more than some U.S. universities, and there is certainly no expectation that a typical applicant will have completed this many courses.

In your case, I expect the main issue will be whether you are applying to pure or applied math departments, since combinatorics could be located in either.  For pure mathematics, the admissions committee will wonder how many of your courses were based on rigorous proofs (for example, applied complex variables and mathematical methods for sciences courses might not be), so it would be best to be clear about that.

I would recommend applying broadly and seeing what happens.  Even if your coursework is not ideal, you may still be admitted, with the expectation of having to catch up in a few topics.  Ultimately, it depends on how compelling your application is overall, and your transcript will be just one factor.