About $\kappa$-Knaster and $\kappa$-linked

Question

For an infinite cardinal $\kappa$ and a partial order $\mathbb{P}$, we say:

(1) $\mathbb{P}$ has the $\kappa$-linked is a union of $\kappa$-many linked subsets.

(2) $\mathbb{P}$ has the $\kappa$-Knaster property iff for every $A \subseteq \mathbb{P}$ of size $\kappa$ there is $B \subseteq A$ of size $\kappa$ consisting of pairwise compatible elements.

Question : If $\mathbb{P}$ is $\kappa$-linked is it $\kappa^{+}$-Knaster?

Answer 1

Turning my awesome comment into answer.

WLOG $|\mathbb{P}| \geq \kappa^{+}$. Say $A \subseteq \mathbb{P}$ has size $\kappa^+$. Since $\mathbb{P}$ can be written as a $\kappa$ union of linked sets one of these linked sets must meet $A$ at $\kappa^+$ many points. So P is $\kappa^+$ Knaster.