论文标题
证明有关连通性的猜想，保持在k连接的两分图中的奇数路径
Proof a conjecture on connectivity keeping odd paths in k-connected bipartite graphs
论文作者
论文摘要
Luo，Tian and Wu（2022）猜想，对于任何树$ t $带有两人$ x $和$ y $，每个$ k $ contect的二键$ g $，具有至少$ k+t $，至少$ k+t $，其中$ t = $ t = $ t = $ max $ \ \ \ x | x | x | y | y | | \ y | \ y | $ k $ - 连接。请注意，当树$ t $是订单$ m $的路径时，$ t = \ lceil \ frac {m} {2} \ rceil $。在本文中，我们证明了至少$ k+ \ lceil \ frac {m+ 1} {2} {2} {2} \ rceil $包含一个$ g-v（p）$ k $ k $连接的每个$ k $连接的两分图$ g $，至少至少$ k+ \ \ lceil \ frac {m+ 1} {2} {2} \ rceil $包含$ g-v（p）$ k $ contected。这表明该猜想对于具有奇数的路径是正确的。对于具有均匀顺序的路径，本文中绑定的最低度是猜想中的结合。
Luo, Tian and Wu (2022) conjectured that for any tree $T$ with bipartition $X$ and $Y$, every $k$-connected bipartite graph $G$ with minimum degree at least $k+t$, where $t=$max$\{|X|,|Y|\}$, contains a tree $T'\cong T$ such that $G-V(T')$ is still $k$-connected. Note that $t=\lceil\frac{m}{2}\rceil$ when the tree $T$ is the path with order $m$. In this paper, we proved that every $k$-connected bipartite graph $G$ with minimum degree at least $k+ \lceil\frac{m+1}{2}\rceil$ contains a path $P$ of order $m$ such that $G-V(P)$ remains $k$-connected. This shows that the conjecture is true for paths with odd order. And for paths with even order, the minimum degree bound in this paper is the bound in the conjecture plus one.
