论文标题
在$ k $连接的图中的两个最长路径的交集
On the intersection of two longest paths in $k$-connected graphs
论文作者
论文摘要
我们表明，$ N $顶点上的$ K $连接图中的每对最长路径至少在$（8K-N+2）/5 $顶点相交。我们还表明，在4个连接的图中，每对最长的路径至少在至少四个顶点中相交。这证实了当$ k $连接的图表$ k \ leq 4 $或$ k \ geq（n-2）/3 $时，以$ k $连接的图为hippchen的猜想。
We show that every pair of longest paths in a $k$-connected graph on $n$ vertices intersect each other in at least $(8k-n+2)/5$ vertices. We also show that, in a 4-connected graph, every pair of longest paths intersect each other in at least four vertices. This confirms a conjecture of Hippchen for $k$-connected graphs when $k\leq 4$ or $k\geq (n-2)/3$.
