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Node-and edge-deletion NP-complete problems
Open accessAbstract
If π is a graph property, the general node(edge) deletion problem can be stated as follows: Find the minimum number of nodes(edges), whose deletion results in a subgraph satisfying property π. In this paper we show that if π belongs to a rather broad class of properties (the class of properties that are hereditary on induced subgraphs) then the node-deletion problem is NP-complete, and the same is true for several restrictions of it. For the same class of properties, requiring the remaining graph to be connected does not change the NP-complete status of the problem; moreover for a certain subclass, finding any "reasonable" approximation is also NP-complete. Edge-deletion problems seem to be less amenable to such generalizations. We show however that for several common properties (e.g. planar, outer-planar, line-graph, transitive digraph) the edge-deletion problem is NP-complete.
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Cites
The complexity of theorem-proving procedures
Cook, S. A. (1971) · Proceedings of the third annual ACM symposium on Theory of computing - STOC '71 · doi:10.1145/800157.805047 · Cited by 6,385
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On the computational complexity of Ising spin glass models
Barahona, F. (1982) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/15/10/028 · Cited by 1,306
Coherent Ising machine based on degenerate optical parametric oscillators
Wang, Z., Marandi, A., Wen, K., Byer, R. L., & Yamamoto, Y. (2013) · Physical Review A · doi:10.1103/physreva.88.063853 · Cited by 391
The maximum edge biclique problem is NP-complete
Peeters, R. (2003) · Discrete Applied Mathematics · doi:10.1016/s0166-218x(03)00333-0 · Cited by 374
Finding a Maximum Clique in an Arbitrary Graph
Balas, E., & Yu, C. S. (1986) · SIAM Journal on Computing · doi:10.1137/0215075 · Cited by 295
A study of the performance of classical minimizers in the Quantum Approximate Optimization Algorithm
Fernández-Pendás, M., Combarro, E. F., Vallecorsa, S., Ranilla, J., & Rúa, I. F. (2022) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2021.113388 · Cited by 52
Metadata
- Authors
- Yannakakis, M.
- Venue
- Proceedings of the tenth annual ACM symposium on Theory of computing - STOC '78
- Publisher
- ACM Press
- Published
- 1978
- Pages
- 253-264
- OpenAlex
- W2045027193
- Cited by
- 435
- References
- 1
- FWCI
- 2.33
- Type
- conference paper
- Language
- en
- Open access
- bronze
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- Yannakakis, M. (1978). Node-and edge-deletion NP-complete problems. Proceedings of the tenth annual ACM symposium on Theory of computing - STOC '78. https://doi.org/10.1145/800133.804355
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