Optimal budget constant for minimum-degree strategies

Determine the optimal value of the constant governing successful strategies at the hitting time for minimum degree at least k in the budget-constrained random graph process.

Background

The paper summarizes prior work showing that, for fixed k, successful strategies can achieve the hitting time for minimum degree at least k with linear budget. A strategy at the exact hitting time uses a constant C_k in the budget, with known bounds on C_k, but the optimal constant has not been determined.

References

The optimal value that this constant may take remains unknown.

— Graph factors and powers of Hamilton cycles in the budget-constrained random graph process  (2502.20870 - Díaz et al., 28 Feb 2025) in Section 1, subsection “Previous results”