# Computing the atom graph of a graph and the union join graph of a hypergraph

11 Jul 2016 Berry Anne Simonet Geneviève

The atom graph of a graph is the graph whose vertices are the atoms obtained by clique minimal separator decomposition of this graph, and whose edges are the edges of all possible atom trees of this graph. We provide two efficient algorithms for computing this atom graph, with a complexity in $O(min(n^\alpha \log n, nm, n(n+\overline{m}))$ time, which is no more than the complexity of computing the atoms in the general case... (read more)

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• DATA STRUCTURES AND ALGORITHMS
• DISCRETE MATHEMATICS