Connectivity for kite-linked graphs

For a given graph H, a graph G is H-linked if, for every injection phi : V (H) -> V (G), the graph G contains a subdivision of H with phi(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.