Bound the ratio for axis-parallel rectangle intersection graphs

Determine whether the domination-packing ratio \(\gamma(G)/\rho(G)\) is bounded by a constant for intersection graphs of axis-parallel rectangles in the plane.

Background

The paper identifies geometric intersection graph classes as a further source of unresolved bounded-ratio questions. In particular, it explicitly lists intersection graphs of axis-parallel rectangles in the plane as a class for which no constant bound on γ(G)/ρ(G)\gamma(G)/\rho(G) is known.

References

The question of bounding the ratio $\gamma/\rho$ for graphs in many geometric graph classes remains open as well. For example, intersection graphs of axis-parallel rectangles in the plane or intersection graphs of axis-parallel boxes in three dimensions.

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