Dendrites and chaos

We answer the two questions left open in [Z.~Ko\v{c}an, Internat. J. Bifur. Chaos Appl. Sci. Engrg. $\mathbf{\text{22}}$, 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 $\mathit{\text{DC3}}$ 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 $\mathit{\text{DC1}}$ pairs.