  We answer the two questions left open in [Z.~Ko\v{c}an, Internat. J. Bifur.
Chaos Appl. Sci. Engrg. \textbf{22}, article id: 125025 (2012)] i.e. whether
there is a relation between $\omega$-chaos and distributional chaos and whether
there is a relation between an infinite LY-scrambled set and distributional
chaos for dendrite maps. We construct a continuous self-map of dendrite without
any \textit{DC3} pairs but containing an uncountable $\omega$-scrambled set. To
answer for the second question we construct dendrite $\mathcal{D}$ and
continuous dendrite map without an infinite LY-scrambled set but with
\textit{DC1} pairs.
