NP-Completeness of graph decomposition problems

The H-decomposition problem for a fixed graph H is stated as follows: Can an input graph G be represented as an edge disjoint union of subgraphs, all of which are isomorphic to H? Although H-decomposition problems have been the subject of extensive mathematical research for many decades, even the co...

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Bibliographic Details
Published inJournal of Complexity Vol. 7; no. 2; pp. 200 - 212
Main Authors Cohen, Edith, Tarsi, Michael
Format Journal Article
LanguageEnglish
Published Elsevier Inc 1991
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ISSN0885-064X
1090-2708
DOI10.1016/0885-064X(91)90006-J

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Summary:The H-decomposition problem for a fixed graph H is stated as follows: Can an input graph G be represented as an edge disjoint union of subgraphs, all of which are isomorphic to H? Although H-decomposition problems have been the subject of extensive mathematical research for many decades, even the complexity status of such problems is yet unknown, except for a few families of graphs. H. I. Holyer conjectured that H-decomposition is NP-complete whenever H is connected and has at least 3 edges. The above was proved, however, only for a limited class of graphs H: complete graphs, simple paths, and simple circuits. Holyer's conjecture is proved here for a large family of graphs which contains all trees.
ISSN:0885-064X
1090-2708
DOI:10.1016/0885-064X(91)90006-J