论文标题
注意连接性保持蜘蛛在$ k $连接的图中
Note on the connectivity keeping spiders in $k$-connected graphs
论文作者
论文摘要
W. Mader [J. Graph Deoluce 65（2010），61--69]指出，对于任何树的$ t $ t $ m $，每个$ k $连接的图形$ g $，带有$δ（g）\ geq \ lfloor \ lfloor \ frac {3k} {3k} {2} \ rfloor+m-1 $ con $ t $ t $ g- 2010年，Mader确认了$ K $连接的图的猜想，如果$ t $是一条路径；最近，Liu等人。确认了猜想，如果$ k = 2,3 $。猜想以$ k \ geq 4 $开放。在本文中，我们表明，如果$ t $是蜘蛛，而$δ（g）= | g | -1 $，则Mader的猜想是$ K+1 $连接的图形。
W. Mader [J. Graph Theory 65 (2010), 61--69] conjectured that for any tree $T$ of order $m$, every $k$-connected graph $G$ with $δ(G)\geq\lfloor\frac{3k}{2}\rfloor+m-1$ contains a tree $T'\cong T$ such that $G-V(T')$ remains $k$-connected. In 2010, Mader confirmed the conjecture for the $k$-connected graph if $T$ is a path; very recently, Liu et al. confirmed the conjecture if $k=2,3$. The conjecture is open for $k\geq 4$ till now. In this paper, we show that Mader's conjecture is true for the $k+1$-connected graph if $T$ is a spider and $Δ(G)=|G|-1$.
