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Journal of Combinatorial Theory Series B
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Discrete Applied Mathematics
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ACM Transactions on Algorithms (TALG)
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ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
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APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
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Journal of Combinatorial Theory Series B
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An H-decomposition of a graph G = (V,E) is a partition of E into subgraphs isomorphic to H. Given a fixed graph H, the H-decomposition problem is to determine whether an input graph G admits an H-decomposition.I. Holyer (1980) conjectured that H-decomposition is Np-complete whenever H is connected and has at least 3 edges. Some partial results have been obtained during the last decade. A complete proof for Holyer's conjecture is the content of this paper.