胖三角连杆与风筝连杆图
Fat-triangle linkage and kite-linked graphs
摘要：
对于一个多重图$H$，如果每个单射映射$ϕ: V(H)\to V(G)$都能扩张到$G$中的一个$H$ -剖分，则称$G$是$H$ -连通的.我们研究了一个图是$H$ -链接的所需的最小连通度。$k$ -胖三角形$F_k$是一个有三个顶点和总共有$k$条边的多重图。我们确定了一个明确的连通性要求的图是$F_k$链接。特别地，当$F_k$连通时，任何$k$连通图都是$F_k$-链接的.风筝是从$K_4$中去掉顶点处的两条边而得到的图。作为$F_k$ -连接的一个非平凡应用，我们证明了每个$8$ -连通图都是风筝连接的，这说明了一个图要风筝连接所需的连通度是$7$或$8$ .
英文摘要：
For a multigraph $H$, a graph $G$ is $H$-linked if every injective mapping $ϕ: V(H)\to V(G)$ can be extended to an $H$-subdivision in $G$. We study the minimum connectivity required for a graph to be $H$-linked. A $k$-fat-triangle $F_k$ is a multigraph with three vertices and a total of $k$ edges. We determine a sharp connectivity requirement for a graph to be $F_k$-linked. In particular, any $k$-connected graph is $F_k$-linked when $F_k$ is connected. A kite is the graph obtained from $K_4$ by removing two edges at a vertex. As a nontrivial application of $F_k$-linkage, we then prove that every $8$-connected graph is kite-linked, which shows that the required connectivity for a graph to be kite-linked is $7$ or $8$.
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