Three-dimensional quartic Yukawa power-counting identity ($\omega =3-b/2-f-n_4$)

For a connected amputated Feynman diagram with the quartic Yukawa interaction in three spacetime dimensions, scalar quartic and scalar sextic vertices, $b$ external bosonic legs, $f$ external fermionic legs and $n_4$ scalar quartic vertices, the superficial degree of divergence is the displayed expression. Indeed $\omega =3L-2I_b-I_f$, $2I_b+b=2n_Y+4n_4+6n_6$, $2I_f+f=2n_Y$ and $L=I_b+I_f-n_Y-n_4-n_6+1$. Substitution eliminates the counts of the two marginal vertices. The bound concerns overall ultraviolet divergence, before numerator cancellations and subtraction of ultraviolet subdivergences.