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A Separator Theorem for Planar Graphs
Abstract
Let G be any n-vertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than ${2n / 3}$ vertices, and C contains no more than $2\sqrt 2 \sqrt n $ vertices. We exhibit an algorithm which finds such a partition A, B, C in $O( n )$ time.
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Bast, H., Delling, D., Goldberg, A., Müller-Hannemann, M., Pajor, T., Sanders, P., Wagner, D., & Werneck, R. F. (2016) · Lecture Notes in Computer Science · doi:10.1007/978-3-319-49487-6_2 · Cited by 610
Metadata
- Authors
- Lipton, R. J., & Tarjan, R. E.
- Venue
- SIAM Journal on Applied Mathematics
- Published
- 1979-04
- Volume
- 36
- Issue
- 2
- Pages
- 177-189
- ISSN
- 0036-1399 (ISSN-L)
- 1095-712X
- OpenAlex
- W2038643780
- Cited by
- 1,359
- References
- 0
- FWCI
- 13.43
- Type
- journal article
- Language
- en
- Open access
- closed
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- Lipton, R. J., & Tarjan, R. E. (1979). A Separator Theorem for Planar Graphs. SIAM Journal on Applied Mathematics. https://doi.org/10.1137/0136016
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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.
