Decremental 2- and 3-Connectivity on Planar Graphs

We study the problem of maintaining the 2-edge-, 2-vertex-, and 3-edge-connected components of a dynamic planar graph subject to edge deletions. The 2-edge-connected components can be maintained in a total of O(n log n) time under any sequence of at most O(n) deletions. This gives O(log n) amortized time per deletion. The 2-vertex- and 3-edge-connected components can be maintained in a total of O(n log2 n) time. This gives O(log2 n) amortized time per deletion. The space required by all our data structures is O(n). All our time bounds improve previous bounds.