Bound the domination-packing ratio for homogeneously orderable and chordal bipartite graphs

Determine whether the ratio \(\gamma(G)/\rho(G)\) is bounded by a constant over the classes of homogeneously orderable graphs and chordal bipartite graphs.

Background

The paper places homogeneously orderable and chordal bipartite graphs among graph classes for which the boundedness of the domination-packing ratio has not been established. The open issue is whether a class-dependent constant bounds γ(G)/ρ(G)\gamma(G)/\rho(G) for every graph in either class.

References

From previous works, the complete resolution of Conjecture $\ref{conj:deg3}$ and bounding the ratio $\gamma/\rho$ for homogeneously orderable and chordal bipartite graphs remain open.

— On graph classes with constant domination-packing ratio  (2503.05562 - Bonamy et al., 7 Mar 2025) in Section 7, Conclusion