Dynamic representations of sparse graphs

Abstract

We present a linear space data structure for maintaining graphs with bounded arboricity-a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth-under edge insertions, edge deletions, and adjacency queries. The data structure supports adjacency queries in worst case O(c) time, and edge insertions and edge deletions in amortized O(1) and O(c+log n) time, respectively, where n is the number of nodes in the graph, and c is the bound on the arboricity.