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Graph Decomposition is NP-Complete: A Complete Proof of Holyer's Conjecture

Authors:

Dorit Dor,

Michael TarsiAuthors Info & Claims

SIAM Journal on Computing, Volume 26, Issue 4

Pages 1166 - 1187

https://doi.org/10.1137/S0097539792229507

Published: 01 August 1997 Publication History

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Abstract

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.In 1980, Holyer conjectured that H-decomposition is NP-complete whenever H is connected and has three edges or more. Some partial results have been obtained since then. A complete proof of Holyer's conjecture is the content of this paper. The characterization problem of all graphs H for which H-decomposition is NP-complete is hence reduced to graphs where every connected component contains at most two edges.

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https://dl.acm.org/doi/10.1007/s10878-024-01112-2
Mondal JVijayakumar S(2024)Star Covers and Star Partitions of Cographs and Butterfly-free GraphsAlgorithms and Discrete Applied Mathematics10.1007/978-3-031-52213-0_16(224-238)Online publication date: 15-Feb-2024
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Divya DVijayakumar S(2024)On Star Partition of Split GraphsAlgorithms and Discrete Applied Mathematics10.1007/978-3-031-52213-0_15(209-223)Online publication date: 15-Feb-2024
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Index Terms

Graph Decomposition is NP-Complete: A Complete Proof of Holyer's Conjecture
1. Mathematics of computing
  1. Discrete mathematics
2. Theory of computation
  1. Computational complexity and cryptography
    1. Problems, reductions and completeness

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Published In

SIAM Journal on Computing Volume 26, Issue 4

Aug. 1997

403 pages

ISSN:0097-5397

Editor:
Z. Galil
Columbia Univ., New York, NY; and Tel-Aviv Univ., Tel-Aviv, Israel

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 August 1997

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Mondal JVijayakumar S(2024)Star covers and star partitions of double-split graphsJournal of Combinatorial Optimization10.1007/s10878-024-01112-247:3Online publication date: 22-Mar-2024
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Mondal JVijayakumar S(2024)Star Covers and Star Partitions of Cographs and Butterfly-free GraphsAlgorithms and Discrete Applied Mathematics10.1007/978-3-031-52213-0_16(224-238)Online publication date: 15-Feb-2024
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Decomposition of complete graphs into paths and stars

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