More on limited packings in graphs

Xuqing Bai (), Hong Chang () and Xueliang Li ()
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Xuqing Bai: Nankai University
Hong Chang: Nankai University
Xueliang Li: Nankai University

Journal of Combinatorial Optimization, No 0, 19 pages

Abstract: 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 $$L_k(G)$$Lk(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.

Keywords: k-limited packing; Opening packing; Nordhaus–Gaddum type result; 05C69; 05C70 (search for similar items in EconPapers)
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DOI: 10.1007/s10878-020-00606-z

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