Faster Fully-Dynamic Minimum Spanning Forest
  We give a new data structure for the fully-dynamic minimum spanning forest problem in simple graphs. Edge updates are supported in $O(\log^4n/\log\log n)$ amortized time per operation, improving the $O(\log^4n)$ amortized bound of Holm et al. (STOC'98, JACM'01). We assume the Word-RAM model with standard instructions. 
Jacob Holm, Eva Rotenberg, Christian Wulff-Nilsen
cs.DS