  In this short survey we present the appearance of some combinatorial notions
in quantum field theory. We first focus on topological graph polynomials (the
Tutte polynomial and its multivariate version) and their relation with the
parametric representation of the commutative $\Phi^4$ field theory. We then
generalize this to ribbon graphs and present the relation of the
Bollob\'as-Riordan polynomial with the parametric representation of some
$\Phi^4$ field theory on the non-commutative Moyal space. We also review the
r\^ole played by the Connes-Kreimer Hopf algebra as the combinatorial backbone
of the renormalization process in field theories. We then show how this
generalizes to the scalar $\Phi^4$ field theory implemented on the
non-commutative Moyal space. Finally, some perspectives for the further
generalization of these tools to quantum gravity tensor models are briefly
sketched.
