For a given graph $H$, a graph $G$ is H-linked if, for every injection $\varphi: V(H) \to V(G)$, the graph $G$ contains a subdivision of $H$ with $\varphi(v)$ corresponding to $v$ for each $v\in V(H)$. Let $f(H)$ be the minimum integer $k$ such that every $k$-connected graph is $H$-linked. Among connected simple graphs $H$ with at least four vertices, the exact value $f(H)$ is only known when $H$ is a star, or a path with four vertices, or a cycle with four vertices. A kite is the graph obtained from $K_4$ by deleting two adjacent edges, i.e., a triangle together with a pendant edge. The exact value of $f(H)$ when $H$ is the kite remains open. In this paper, we settle this problem by showing that every 7-connected graph is kite-linked.

A proper vertex coloring of a graph G is equitable if the sizes of color classes differ by at most one. The equitable chromatic threshold $\chi_{eq}^*(G)$ of G is the smallest integer m such that G is equitably n-colorable for all $n\geq m$. We show that for planar graphs G with minimum degree at least two, $\chi_{eq}^*(G)\leq4$ if the girth of G is at least 10, and $\chi_{eq}^*(G)\leq3$ if the girth of G is at least 14.