Minimum degree for cliques with arbitrary bias

Determine s_{MB}^b(K_t) for every pair of positive integers b and t.

Background

For cliques, the paper determines s_{MB}1(K_t)=2t-3. For fixed b\geq2, it only provides bounds of order between bt and bt\ln t, leaving a gap that the authors ask to close.

References

Determine s_{MB}b(K_t) for every b,t\in\mathbb{N}.

— Ramsey-type results for Maker-Breaker games  (2609.02588 - Allin et al., 2 Sep 2026) in Problem following the subsection “Minimal winnable graphs for cliques,” Concluding remarks and open problems

Is the maximum degree among all graphs in \mathcal{M}1_{MB}(K_t) unbounded? If not, what is the largest maximum degree among all graphs in \mathcal{M}1_{MB}(K_t)?

— Ramsey-type results for Maker-Breaker games  (2609.02588 - Allin et al., 2 Sep 2026) in Problem following Theorem 5.1, Concluding remarks and open problems