Dr Vadim Zverovich Vadim.Zverovich@uwe.ac.uk
Associate Professor
The probabilistic approach to limited packings in graphs
Zverovich, Vadim; Gagarin, Andrei
Authors
Andrei Gagarin
Abstract
© 2014 Elsevier B.V. All rights reserved. We consider (closed neighbourhood) packings and their generalization in graphs. A vertex set X in a graph G is a k-limited packing if for every vertex vεV(G), |N[v]∩X|≤k, where N[v] is the closed neighbourhood of v. The k-limited packing number (G) of a graph G is the largest size of a k-limited packing in G. Limited packing problems can be considered as secure facility location problems in networks. In this paper, we develop a new application of the probabilistic method to limited packings in graphs, resulting in lower bounds for the k-limited packing number and a randomized algorithm to find k-limited packings satisfying the bounds. In particular, we prove that for any graph G of order n with maximum vertex degree δ,(G)≥kn(k+1)(δk)(δ+1)k. Also, some other upper and lower bounds for (G) are given.
Citation
Zverovich, V., & Gagarin, A. (2015). The probabilistic approach to limited packings in graphs. Discrete Applied Mathematics, 184, 146-153. https://doi.org/10.1016/j.dam.2014.11.017
Journal Article Type | Article |
---|---|
Publication Date | Jan 1, 2015 |
Publicly Available Date | Jun 6, 2019 |
Journal | Discrete Applied Mathematics |
Print ISSN | 0166-218X |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 184 |
Pages | 146-153 |
DOI | https://doi.org/10.1016/j.dam.2014.11.017 |
Keywords | k-limited packings, the probabilistic method, lower and upper bounds, randomized algorithm |
Public URL | https://uwe-repository.worktribe.com/output/836953 |
Publisher URL | http://dx.doi.org/10.1016/j.dam.2014.11.017 |
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