Dynamic treewidth

We present a data structure that for a dynamic graph G that is updated by edge insertions and deletions, maintains a tree decomposition of G of width at most 6k + 5 under the promise that the treewidth of G never grows above k. The amortized update time is O-k(2(root log n log log n)), where n is the vertex count of G and the O-k(.) notation hides factors depending on k. In addition, we also obtain the dynamic variant of Courcelle's Theorem: for any fixed property phi expressible in the CMSO2 logic, the data structure can maintain whether G satisfies phi within the same time complexity bounds. To a large extent, this answers a question posed by Bodlaender [WG 1993].