Tomas Feder, Rajeev Motwani, An Zhu

We consider the problem of finding a $k$-vertex ($k$-edge)

connected spanning subgraph $K$ of a given $n$-vertex graph $G$

while minimizing the maximum degree $d$ in $K$. We give a

polynomial time algorithm for fixed $k$ that achieves an $O(\log

n)$-approximation. The only known previous polynomial algorithms

achieved degree $d+1$ ...
more >>>