We show that connected graphs admit sublinear longest path transversals. This improves an earlier result of Rautenbach and Sereni and is related to the fifty-year-old question of whether connected graphs admit longest path transversals of constant size. The same technique allows us to show that $2$-connected graphs admit sublinear longest cycle transversals.

翻译：我们展示了连接的图形可以接收最长的亚线性路径。 这改善了Rautenbach和Sereni的早期结果, 并且与连接的图形是否接收最长的、不变大小的路径的五十年问题相关。 同样的技术让我们可以显示, $2 美元连接的图形可以接收最长的子线性路径。