A Dynamic Data Structure for MSO Properties in Graphs with Bounded Tree-Depth

Tree-depth is an important graph parameter which arose in the study of sparse graph classes. We present a dynamic data structure for representing a graph G with tree-depth at most D. The structure allows addition and removal of edges and vertices under assumption that the resulting graph still has tree-depth at most D, in time bounds depending only on D. A tree-depth decomposition of the graph is maintained explicitly.

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