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Lower Bounds for the Partitioning of Graphs
Abstract
Let a k-partition of a graph be a division of the vertices into k disjoint subsets containing m1≥ m2, …, ≥ mkvertices. Let Ecbe the number of edges whose two vertices belong to different subsets. Let λ1≥ λ2, …, ≥ λkbe the k largest eigenvalues of a matrix, which is the sum of the adjacency matrix of the graph plus any diagonal matrix U such that the sum of all the elements of the sum matrix is zero. Then given equation. A theorem is given that shows the effect of the maximum degree of any node being limited, and it is also shown that the right-hand side is a concave function of U. Computational studies are made of the ratio of upper bound to lower bound for the two-partition of a number of random graphs having up to 100 nodes.
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Metadata
- Authors
- Donath, W. E., & Hoffman, A. J.
- Venue
- IBM Journal of Research and Development
- Publisher
- IBM
- Published
- 1973-09
- Volume
- 17
- Issue
- 5
- Pages
- 420-425
- ISSN
- 0018-8646 (ISSN-L)
- OpenAlex
- W2033852356
- Cited by
- 660
- References
- 0
- FWCI
- 0.54
- Type
- journal article
- Language
- en
- Open access
- closed
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