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Product graph representations. (English) Zbl 0766.05092
Author’s abstract: We study a hierarchy of canonical representations of graphs as subgraphs of cartesian products of graphs. This hierarchy starts with the isometric representation, includes the 2-isometric representation, and ends with the cartesian prime factorization. We show that all three representations can be obtained in \(O(mn)\) time using \(O(m)\) space, for graphs with \(n\) vertices and \(m\) edges. The algorithms have immediate parallel versions that use \(n^ 3\) processors and run in \(O(\log^ 2n)\) time.

MSC:
05C99 Graph theory
05C10 Planar graphs; geometric and topological aspects of graph theory
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
68Q25 Analysis of algorithms and problem complexity
68R10 Graph theory (including graph drawing) in computer science
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