The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
Finding a Maximum Clique in an Arbitrary Graph
Abstract
We describe a new type of branch and bound procedure for finding a maximum clique in an arbitrary graph $G = (V,E)$. The two main ingredients, both of $O(|V| + |E|)$ time complexity, are (i) an algorithm for finding a maximal triangulated induced subgraph of G; and (ii) an algorithm for finding a maximal k-chromatic induced subgraph of G. We discuss computational experience on randomly generated graphs with up to 400 vertices and 30,000 edges.
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Cites
Algorithm 457: finding all cliques of an undirected graph
Bron, C., & Kerbosch, J. (1973) · Communications of the ACM · doi:10.1145/362342.362367 · Cited by 2,452
Incidence matrices and interval graphs
Fulkerson, D., & Gross, O. (1965) · Pacific Journal of Mathematics · doi:10.2140/pjm.1965.15.835 · Cited by 1,262
Algorithmic Aspects of Vertex Elimination on Graphs
Rose, D. J., Tarjan, R. E., & Lueker, G. S. (1976) · SIAM Journal on Computing · doi:10.1137/0205021 · Cited by 1,203
Dirac, G. A. (1961) · Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg · doi:10.1007/bf02992776 · Cited by 927
Vertex packings: Structural properties and algorithms
Nemhauser, G. L., & Trotter, L. E. (1975) · Mathematical Programming · doi:10.1007/bf01580444 · Cited by 664
On certain polytopes associated with graphs
Chvátal, V. (1975) · Journal of Combinatorial Theory Series B · doi:10.1016/0095-8956(75)90041-6 · Cited by 604
Finding a Maximum Independent Set
Tarjan, R. E., & Trojanowski, A. E. (1977) · SIAM Journal on Computing · doi:10.1137/0206038 · Cited by 474
Node-and edge-deletion NP-complete problems
Yannakakis, M. (1978) · Proceedings of the tenth annual ACM symposium on Theory of computing - STOC '78 · doi:10.1145/800133.804355 · Cited by 435
Cited by
Pardalos, P. M., & Xue, J. (1994) · Journal of Global Optimization · doi:10.1007/bf01098364 · Cited by 382
Finding Maximum Cliques on the D-Wave Quantum Annealer
Chapuis, G., Djidjev, H., Hahn, G., & Rizk, G. (2019) · Journal of Signal Processing Systems · doi:10.1007/s11265-018-1357-8 · Cited by 70
Metadata
- Authors
- Balas, E., & Yu, C. S.
- Venue
- SIAM Journal on Computing
- Published
- 1986-11
- Volume
- 15
- Issue
- 4
- Pages
- 1054-1068
- ISSN
- 0097-5397 (ISSN-L)
- 1095-7111
- OpenAlex
- W2043005464
- Cited by
- 295
- References
- 8
- FWCI
- 5.73
- Type
- journal article
- Language
- en
- Open access
- closed
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- Balas, E., & Yu, C. S. (1986). Finding a Maximum Clique in an Arbitrary Graph. SIAM Journal on Computing. https://doi.org/10.1137/0215075
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