Comment on “The Steiner number of a graph” by G. Chartrand and P. Zhang: [Discrete Mathematics 242 (2002) 41–54]

We show by counterexample that one of the main results in the paper “The Steiner number of a graph” by Chartrand and Zhang (Disc. Math. 242 (2002) 41–54) does not hold. To be more precise, we prove both that not every Steiner set is a geodetic set and that there are connected graphs whose Steiner number is strictly lower than its geodetic number.