SIAM Journal on Discrete Mathematics, Volume 35, Issue 1, Page 431-446, January 2021.
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.

中文翻译：

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风筝链接图的连通性

SIAM Journal on Discrete Mathematics，第 35 卷，第 1 期，第 431-446 页，2021 年 1 月。
对于给定的图 $H$，如果每次注入 $\varphi：V(H)，则图 $G$ 是 H 关联的\to V(G)$，图$G$ 包含$H$ 的细分，其中$\varphi(v)$ 对应于每个$v\in V(H)$ 的$v$。令 $f(H)$ 是最小整数 $k$，使得每个 $k$-connected 图都是 $H$-linked。在至少有四个顶点的连接简单图 $H$ 中，精确值 $f(H)$ 仅在 $H$ 是星形、或具有四个顶点的路径或具有四个顶点的循环时才知道。风筝是从$K_4$ 中删除两条相邻边得到的图，即一个三角形和一条悬垂边。当 $H$ 是风筝时 $f(H)$ 的确切值保持打开状态。在本文中，我们通过证明每个 7 连通图都是风筝链接来解决这个问题的。