The circumference of a graph $G$ is the length of a longest cycle in $G$, or $+\infty$ if $G$ has no cycle. Birmel\'e (2003) showed that the treewidth of a graph $G$ is at most its circumference minus one. We strengthen this result for $2$-connected graphs as follows: If $G$ is $2$-connected, then its treedepth is at most its circumference. The bound is best possible and improves on an earlier quadratic upper bound due to Marshall and Wood (2015).

翻译：图G$的周长为以G$计算的最长周期的长度,如果G$没有周期,则以$为单位,或以$为单位,则以$为单位。Birmel\'e(2003年)显示,图G$的树边至多是其周长减去1美元。我们用以下2美元的连结图强化这一结果:如果G$是连接了2美元,那么其树的深度最多是其周长。最佳的界限是尽可能的,并且由于Marshall和Wood(2015年)的缘故,其早期的四方形上方的界限会得到改善。