Complete the resolution of the subcubic domination-packing conjecture

Resolve the remaining aspects of the conjecture that every connected graph \(G\) with maximum degree at most 3 satisfies \(\gamma(G)\le 2\rho(G)+1\), together with the prescribed characterization of equality cases.

Background

The paper recalls a conjecture for connected subcubic graphs asserting the bound $\gamma(G)\le 2\rho(G)+1$ and restricting equality to three specified graphs. Its results disprove the claimed restriction on equality cases by constructing an infinite family attaining equality. The authors nevertheless identify the complete resolution of the conjecture as open, so the remaining status of the inequality and its corrected equality characterization is unresolved.