Fully Dynamic Higher Connectivity for Planar Graphs
Keywords and Synonyms
Fully dynamic edge connectivity; Fully dynamic vertex connectivity
In this entry, the problem of maintaining a dynamic planar graph subject to edge insertions and edge deletions that preserve planarity but that can change the embedding is considered. In particular, in this problem one is concerned with the problem of efficiently maintaining information about edge and vertex connectivity in such a dynamically changing planar graph. The algorithms to solve this problem must handle insertions that keep the graph planar without regard to any particular embedding of the graph. The interested reader is referred to the chapter “Fully Dynamic Planarity Testing” of this encyclopedia for algorithms to learn how to check efficiently whether a graph subject to edge insertions and deletions remains planar (without regard to any particular embedding).
Before defining formally the problems considered here, a few preliminary definitions follow.
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