A linear bound for a connectivity partition in graphs

Jia Zhou, Jin Yan, Yunshu Gao

Kühn and Osthus proved that, for every positive integer $\ell$, every $2^{16}{\ell }^2$-connected graph $G$ has a partition $V(G)=S\cup T$ such that $G[S]$ and $G[T]$ are $\ell$-conne…