Abstract
This paper presents a storage method to represent a simple undirected graph, that is, to maintain in a data structure the original graph if m ⩽ n(n − 1) 4 , and the complement graph if m > n(n − 1) 4 . The paper also considers the linear time solvability of some problems based on this storage method. It shows that a breadth first search tree and a depth first search tree on the complement graph of a given graph can be constructed in linear time. It also shows that legal node ordering and sparse subgraphs preserving connectivity properties of the complement graph of a given graph can be found in linear time. By using this procedure, we can solve the problems on complement graphs for determining k-node ( k-edge) connectivity for k ⩽ 3, and constructing a minimal 2-node (2-edge) connected spanning subgraph in linear time.
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