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：我们证明连通图具有次线性最长路横贯。这一结果改进了Rautenbach和Sereni的早期结论，并与一个存在五十年的问题（连通图是否具有常数大小的最长路横贯）相关。相同技术使我们得以证明2-连通图具有次线性最长圈横贯。