  We answer the last question left open in [Z.~Ko\v{c}an, \emph{Chaos on
one-dimensional compact metric spaces}, Internat. J. Bifur. Chaos Appl. Sci.
Engrg. \textbf{22}, article id: 1250259 (2012)] which asks whether there is a
relation between an infinite LY-scrambled set and $\omega$-chaos for dendrite
maps. We construct a continuous self-map of a dendrite without an infinite
LY-scrambled set but containing an uncountable $\omega$-scrambled set.
