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More on limited packings in graphs

Author

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  • Xuqing Bai

    (Nankai University)

  • Hong Chang

    (Nankai University)

  • Xueliang Li

    (Nankai University)

Abstract

A set B of vertices in a graph G is called a k-limited packing if for each vertex v of G, its closed neighbourhood has at most k vertices in B. The k-limited packing number of a graph G, denoted by $$L_k(G)$$ L k ( G ) , is the largest number of vertices in a k-limited packing in G. The concept of the k-limited packing of a graph was introduced by Gallant et al., which is a generalization of the well-known packing of a graph. In this paper, we present some tight bounds for the k-limited packing number of a graph in terms of its order, diameter, girth, and maximum degree, respectively. As a result, we obtain a tight Nordhaus–Gaddum type result for the k-limited packing number. At last, we investigate the relationship among the open packing number, the packing number and 2-limited packing number of trees.

Suggested Citation

  • Xuqing Bai & Hong Chang & Xueliang Li, 2020. "More on limited packings in graphs," Journal of Combinatorial Optimization, Springer, vol. 40(2), pages 412-430, August.
    • Handle: RePEc:spr:jcomop:v:40:y:2020:i:2:d:10.1007_s10878-020-00606-z
    DOI: 10.1007/s10878-020-00606-z
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    References listed on IDEAS

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    1. Dorit S. Hochbaum & David B. Shmoys, 1985. "A Best Possible Heuristic for the k -Center Problem," Mathematics of Operations Research, INFORMS, vol. 10(2), pages 180-184, May.
    2. Doost Ali Mojdeh & Babak Samadi, 2019. "Packing parameters in graphs: new bounds and a solution to an open problem," Journal of Combinatorial Optimization, Springer, vol. 38(3), pages 739-747, October.
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