Abstract. The (independent) chromatic vertex stability vs (ivs) is the minimum size of (independent) set of vertices S, such that deletion of S from a graph decreases its chromatic number. It was conjectured that if the maximum degree is small compared to the chromatic number, than vs=ivs. In the paper we show that (in the order) there are exponentially many graphs, which have chromatic number 3, maximum degree 4, ivs=3 and vs=2. The smallest such graph has order 9 and there are 30 such graphs.