Rationality of weak saturation limits

Prove that the weak saturation limit w_F is rational for every finite graph F.

Background

The paper completely characterizes the rational values that can occur as weak saturation limits and shows that every rational number at least 3/2 is attainable, while values below 3/2 have a more discrete structure. These results do not determine whether an irrational weak saturation limit can occur. The authors therefore conjecture that all weak saturation limits are rational, noting that this would follow from the stronger assertion that sufficiently large minimum weakly F-saturated graphs can be constructed by repeatedly copying a fixed subgraph.

References

Theorem 1.1 raises the natural question of whether weak saturation limits must be rational. We conjecture that the answer is yes. Conjecture 5.2. For any graph F, WF is rational.

— Rational values of the weak saturation limit  (2501.15686 - Ascoli et al., 26 Jan 2025) in Concluding Remarks, Section 5.2, Conjecture 5.2