Edge-connectivity keeping trees in $k$-edge-connected graphs

Qing Yang, Yingzhi Tian

Mader [J. Combin. Theory Ser. B 40 (1986) 152-158] proved that every $k$-edge-connected graph $G$ with minimum degree at least $k+1$ contains a vertex $u$ such that $G-\{u\}$ is st…