2018/07/03 by Xuqing Bai, Bai, Xuqing, Hong Chang +3
Computer Science · Mathematics · #05C69 #05C70 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.1807.01021
openalex publication_date 2018/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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 the tight Nordhaus-Gaddum-type result of this parameter for general k. At last, we investigate the relationship among the open packing number, the packing number and 2-limited packing number of trees.