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The Diameter of a Cycle Plus a Random Matching
Abstract
How small can the diameter be made by adding a matching to an n-cycle? In this paper this question is answered by showing that the graph consisting of an n-cycle and a random matching has diameter about $\log _2 n$, which is very close to the best possible value. It is also shown that by adding a random matching to graphs with certain expanding properties such as expanders or Ramanujan graphs, the resulting graphs have near optimum diameters.
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Citations
Cited by
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Kleinberg, J. (2000) · Proceedings of the thirty-second annual ACM symposium on Theory of computing · doi:10.1145/335305.335325 · Cited by 1,882
Synchronization in Small-World Systems
Barahona, M., & Pecora, L. M. (2002) · Physical Review Letters · doi:10.1103/physrevlett.89.054101 · Cited by 1,638
Networks, Dynamics, and the Small‐World Phenomenon
Watts, D. J. (1999) · American Journal of Sociology · doi:10.1086/210318 · Cited by 1,510
A Survey of Statistical Network Models
Goldenberg, A., Zheng, A. X., Fienberg, S. E., & Airoldi, E. M. (2010) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000005 · Cited by 819
Small-World Phenomena and the Dynamics of Information
Kleinberg, J. (2002) · Advances in Neural Information Processing Systems 14 · doi:10.7551/mitpress/1120.003.0060 · Cited by 382
Metadata
- Authors
- Bollobás, B., & Chung, F. R. K.
- Venue
- SIAM Journal on Discrete Mathematics
- Published
- 1988-08
- Volume
- 1
- Issue
- 3
- Pages
- 328-333
- ISSN
- 0895-4801 (ISSN-L)
- 1095-7146
- OpenAlex
- W2151221105
- Cited by
- 176
- References
- 0
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- closed
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How to cite
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- CoChat. (2026). Citation check: The Diameter of a Cycle Plus a Random Matching. https://app.cochat.ai/papers/10.1137/0401033
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- Bollobás, B., & Chung, F. R. K. (1988). The Diameter of a Cycle Plus a Random Matching. SIAM Journal on Discrete Mathematics. https://doi.org/10.1137/0401033
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
