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Lower bounds on the $k$-limited packing number of a graph | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 23 مرداد 1404 اصل مقاله (355.89 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30589.2546 | ||
| نویسندگان | ||
| Michael A. Henning1؛ Nader Jafari Rad* 2 | ||
| 1Department of Mathematics and Applied Mathematics, University of Johannesburg Auckland Park, 2006 South Africa | ||
| 2Department of Mathematics, Shahed University, Tehran, Iran | ||
| چکیده | ||
| For a given integer $k \ge 1$, a subset $S$ of vertices of a graph $G$ is a $k$-limited packing if $|N_G[v] \cap S| \le k$ for all $v\in V(G)$, where $N_G[v]$ denotes the closed neighborhood of a vertex~$v$ in $G$. The $k$-limited packing number, $L_k(G)$, is the maximum cardinality of a $k$-limited packing in $G$. In this paper we present a probabilistic lower bound for the $k$-limited packing number of a graph. In particular we improve a previous lower bound given in [Discrete Appl. Math. 184 (2015), 146--153]. We also present a randomized algorithm for the $k$-limited packing number of a graph. | ||
| کلیدواژهها | ||
| $k$-limited packing number؛ Probabilistic methods؛ domination | ||
| مراجع | ||
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[9] M. Mohammadi, N. Jafari Rad, and M. Maghasedi, A new probabilistic lower bound on the limited packing number of a graph, Util. Math. 114 (2020), 249–254.
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[12] B. Samadi, On the k-limited packing numbers in graphs, Discrete Optim. 22 (2016), 270–276. https://doi.org/10.1016/j.disopt.2016.08.002 | ||
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