I have been working on what I call a hard science fiction zombie apocalypse novel, but I'm having trouble nailing down the exact genre(s) in which my story could be marketed. My concern is that I don't want to approach a literary agent or publisher with my story, only to get a rejection because it does not cater to the genres which they deal with. So far I've done some scant research online, but what I found wasn't entirely helpful. My questions are: What defines a genre, and is it possible to pitch my novel to an agent or publisher if the novel does not entirely concern itself with the genres they deal with?
Sci-fi/fantasy fiction. It's really as simple as that. But if you want a set genre, I'd go with sci-fi, since zombies (could) exist, but anything hard-fantasy like demons, dragons, etc. would be borderline fantasy.
It is basic sci-fi and if I placed it anywhere it would be in with the growing zombie sub-catagory. Believe me if it doesn't exist already it will soon.
You can just write your story and not worry too much about how it is categorized. That said, if you want to write a hard science fiction story, if that is your goal, then you need to nail down the science. That will distinguish the work from fantasy.
As people above have said it would probably be roughly classed as sci-fi but I wouldn't worry too much if it crosses over with one, two or more other genres as most of the best books incorporate several genres anyway.
Finish writing it first. Then decide what genre you will market it as. If you can't decide even then, submit it to more than one market. Hell, maybe it will end up as horror, or humor.