I've been reading Zee's QFT textbook and trying to follow some lecture notes online whenever I can't grasp something. I really don't understand one thing regarding the renormalization of theories, though.
The two theories commonly used as examples of renormalizable theories are $\phi^3$ in 6 dimensions and $\phi^4$ in 4 dimensions. Apparently, $\phi^3$ can have diagrams with an odd number of external legs, but $\phi^4$ only has even terms. I don't understand where this comes from. I have assumed that even-powered theories would have even terms only, but then I started reading these 2014 lecture notes (section 2.1, p. 24) by John McGreevy and the given example for a $\phi^6$ theory is a three-legged diagram:
which made me a bit confused. How do you actually determine which diagrams are allowed in a theory?