Degeneracy bound for fractional DP-coloring of K_{1,t,t}-free graphs

Establish whether there exists an absolute constant C such that every d-degenerate K_{1,t,t}-free graph G satisfies chi_DP(G) <= C d/log d, uniformly over t.

Background

The paper proves a fractional DP-chromatic bound of order t d/log d for d-degenerate K_{1,t,t}-free graphs, with a leading constant depending linearly on t. In contrast, an earlier result cited by the authors gives an ordinary DP-chromatic bound of order Delta/log Delta with a leading constant independent of t.

The authors ask whether the dependence on t can be eliminated when maximum degree is replaced by degeneracy in the fractional DP-coloring setting.

References

Does there exist an absolute constant $C > 0$ such that $(G) \le C\frac{d}{\log d}$ for every $d$-degenerate $K_{1, t, t}$-free graph $G$?

— Fractional DP-colorings of $d$-degenerate locally sparse graphs  (2609.10978 - Dhawan et al., 10 Sep 2026) in Section 5, Concluding Remarks; Question environment