On a conjecture of Gentner and Rautenbach

Gentner and Rautenbach conjectured that the size of a minimum zero forcing set in a connected graph on n n vertices with maximum degree 3 3 is at most 1 3 n + 2 . We disprove this conjecture by constructing a collection of connected graphs {G n } { G n } with maximum degree 3 of arbitrarily large order having zero forcing number at least 4 9 | V ( G n ) | .