Some properties of $\{k\}$-packing function problem in graphs

Abstract

The recently introduced {k}-packing function problem is considered in this paper. Special relation between a case when k = 1, k ≥ 2 and linear programming relaxation is introduced with sufficient conditions for optimality. For arbitrary simple connected graph G there is construction procedure for finding values of k for which L {k} (G) can be determined in the polynomial time. Additionally, relationship between {1}-packing function and independent set number is established. Optimal values for some special classes of graphs and general upper and lower bounds are introduced.