Equality of feasible pairs for f and g

Determine whether the feasible pairs are identical for the functions f and g.

Background

Complementation transfers many feasible pairs between f and g under membership hypotheses, as shown in Proposition 10.17. The full equality of the two feasible-pair classes remains unresolved.

References

Problem 10.16. Are the feasible pairs the same for f and for g? It seems plausible to guess that the answer is affirmative.

— Monochromatic graph decompositions and monochromatic piercing inspired by anti-Ramsey colorings  (2501.09342 - Caro et al., 16 Jan 2025) in Problem 10.16, Section 10.1