摘要：We present a decremental data structure for maintaining the SPQR-tree of a planar graph subject to edge contractions and deletions. The update time, amortized over Omega(n) operations, is O(log^2 n). Via SPQR-trees, we give a decremental data structure for maintaining 3-vertex connectivity in planar graphs. It answers queries in O(1) time and processes edge deletions and contractions in O(log^2 n) amortized time. The previous best supported deletions and insertions in O(sqrt{n}) time.
关键词：Graph embeddings; data structures; graph algorithms; planar graphs; SPQR-trees; triconnectivity
