Tightness of the Kostochka–Stocker 5/14 bound for large cubic graphs

Determine whether there exist connected cubic graphs of arbitrarily large order n whose domination number attains the Kostochka–Stocker upper bound, that is, establish whether there are connected cubic graphs G with γ(G) = (5/14) |V(G)| for arbitrarily large |V(G)|.

Background

Kostochka and Stocker (2009) proved that every connected cubic graph G of order n satisfies γ(G) ≤ (5/14)n, currently the best general upper bound for such graphs. Despite this advance, it remains unclear whether this bound is tight for large instances.

The authors explicitly note that it is unknown whether graphs of large order achieve this 5/14 bound. Resolving this would clarify the sharpness of the best-known general upper bound and potentially guide future improvements or matching constructions.