Algorithms – Algorithmic complexity of deciding on the existence of regular $ mathrm {f} $ factors in charts

to find regularly $ mathrm {f} $Non-directional simple-charting factors can be reduced to finding a perfect match by using the gadgets of Tutte or Lovasz and Plummer. There are several algorithms for split and general diagrams. So far, however, I have not seen any algorithms that implement the necessary and sufficient conditions of Tutte for the existence of a perfect match.

Question:
calculates a maximum matching to the most efficient way about the existence of a $ mathrm {f} $-Factor
or can the existence of a $ mathrm {f} $Factor be decided more efficiently?