A new probabilistic lower bound on the limited packing number of a graph

Abstract

A set of vertices B C V(G) is called a fc-limited packing set in G if \N[v) n B < k for all v V(G), where k > 1. The k-limited packing number, Lk(G), is the largest number of vertices in a fc-limited packing set. In this paper we present a new probabilistic lower bound for the fc-limited packing number of a graph and improve previous lower bound given in [A.V. Gagarin and V.E. Zverovich, The probabilistic approach to limited packings in graphs, Discrete Appl. Math. 184 (2015), 146-153]. © 2020 Utilitas Mathematica Publishing Inc.. All rights reserved.