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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| Published in | Journal of Complexity Vol. 7; no. 2; pp. 200 - 212 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
1991
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| Online Access | Get full text |
| ISSN | 0885-064X 1090-2708 |
| DOI | 10.1016/0885-064X(91)90006-J |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Tarsi, Michael Cohen, Edith |
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| Cites_doi | 10.1515/crll.1853.45.181 10.1007/BF01956769 10.1137/0210054 10.1007/BF01903577 |
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| References | Holyer (BIB9) 1981; 10 Kirkpatric, Hell (BIB10) 1978 Alon (BIB1) 1983; 42 Bermond, Sotteau (BIB2) 1975 Brouwer, Wilson (BIB4) 1980 Steiner (BIB11) 1853; 45 Caro (BIB5) 1985 Wilson (BIB12) 1976 Holyer (BIB8) 1980 Favaron, Lonc, Truszczynski (BIB6) 1985; 20 Bialostocki, Roditty (BIB3) 1982; 40 Garey, Johnson (BIB7) 1979 Garey (10.1016/0885-064X(91)90006-J_BIB7) 1979 Kirkpatric (10.1016/0885-064X(91)90006-J_BIB10) 1978 Steiner (10.1016/0885-064X(91)90006-J_BIB11) 1853; 45 Bermond (10.1016/0885-064X(91)90006-J_BIB2) 1975 Holyer (10.1016/0885-064X(91)90006-J_BIB9) 1981; 10 Wilson (10.1016/0885-064X(91)90006-J_BIB12) 1976 Holyer (10.1016/0885-064X(91)90006-J_BIB8) 1980 Favaron (10.1016/0885-064X(91)90006-J_BIB6) 1985; 20 Bialostocki (10.1016/0885-064X(91)90006-J_BIB3) 1982; 40 Brouwer (10.1016/0885-064X(91)90006-J_BIB4) 1980 Alon (10.1016/0885-064X(91)90006-J_BIB1) 1983; 42 Caro (10.1016/0885-064X(91)90006-J_BIB5) 1985 |
| References_xml | – start-page: 53 year: 1975 end-page: 72 ident: BIB2 article-title: Graph decomposition and G-designs publication-title: Proceedings of the 5th British Combinatorial Conference – year: 1978 ident: BIB10 article-title: On the completeness of a generalized matching problem publication-title: 10th Annual ACM Symposium on Theory of Computing Machinery – start-page: 647 year: 1976 end-page: 695 ident: BIB12 article-title: Decomposition of a complete graph into subgraphs isomorphic to a given graph publication-title: Utilitas Math. – volume: 10 start-page: 713 year: 1981 end-page: 717 ident: BIB9 article-title: The NP-completeness of some edge partition problems publication-title: Siam J. Comput. – year: 1985 ident: BIB5 article-title: Decomposition and Partition of Trees into Isomorphic Subtrees publication-title: M.Sc Thesis – volume: 45 start-page: 181 year: 1853 end-page: 182 ident: BIB11 article-title: Combinatorische aufgabe publication-title: Z. Reine Angew. Math. – volume: 42 start-page: 221 year: 1983 end-page: 223 ident: BIB1 article-title: A note on the decomposition of graphs into isomorphic matchings publication-title: Acta Math. Hungar. – volume: 20 start-page: 125 year: 1985 end-page: 146 ident: BIB6 article-title: Decomposition of graphs into graphs with three edges publication-title: Ars Combin. – year: 1979 ident: BIB7 article-title: Computers and Intractability, a Guide to the Theory of NP-Completeness – volume: 40 start-page: 201 year: 1982 end-page: 208 ident: BIB3 article-title: 3 publication-title: Acta Math. Acad. Sci. Hungar. – year: 1980 ident: BIB8 article-title: The Complexity of Graph Theory Problems publication-title: Ph.D. dissertation – year: 1980 ident: BIB4 article-title: The Decomposition of Graphs into Ladder Graphs publication-title: Stitching mathematisch centrum (zn 97/80) – volume: 20 start-page: 125 year: 1985 ident: 10.1016/0885-064X(91)90006-J_BIB6 article-title: Decomposition of graphs into graphs with three edges publication-title: Ars Combin. – volume: 45 start-page: 181 year: 1853 ident: 10.1016/0885-064X(91)90006-J_BIB11 article-title: Combinatorische aufgabe publication-title: Z. Reine Angew. Math. doi: 10.1515/crll.1853.45.181 – year: 1980 ident: 10.1016/0885-064X(91)90006-J_BIB8 article-title: The Complexity of Graph Theory Problems – year: 1978 ident: 10.1016/0885-064X(91)90006-J_BIB10 article-title: On the completeness of a generalized matching problem – start-page: 53 year: 1975 ident: 10.1016/0885-064X(91)90006-J_BIB2 article-title: Graph decomposition and G-designs – volume: 42 start-page: 221 year: 1983 ident: 10.1016/0885-064X(91)90006-J_BIB1 article-title: A note on the decomposition of graphs into isomorphic matchings publication-title: Acta Math. Hungar. doi: 10.1007/BF01956769 – year: 1979 ident: 10.1016/0885-064X(91)90006-J_BIB7 – volume: 10 start-page: 713 year: 1981 ident: 10.1016/0885-064X(91)90006-J_BIB9 article-title: The NP-completeness of some edge partition problems publication-title: Siam J. Comput. doi: 10.1137/0210054 – start-page: 647 year: 1976 ident: 10.1016/0885-064X(91)90006-J_BIB12 article-title: Decomposition of a complete graph into subgraphs isomorphic to a given graph publication-title: Utilitas Math. – year: 1980 ident: 10.1016/0885-064X(91)90006-J_BIB4 article-title: The Decomposition of Graphs into Ladder Graphs – volume: 40 start-page: 201 year: 1982 ident: 10.1016/0885-064X(91)90006-J_BIB3 article-title: 3K2-decomposition of a graph publication-title: Acta Math. Acad. Sci. Hungar. doi: 10.1007/BF01903577 – year: 1985 ident: 10.1016/0885-064X(91)90006-J_BIB5 article-title: Decomposition and Partition of Trees into Isomorphic Subtrees |
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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... |
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