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arXiv · 1803.03147

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

Jozef J. Kratica·Aleksandar Lj. Savić·Zoran Lj. Maksimović
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Abstract

The recently introduced $\{k\}$-packing function problem is considered in this paper. Special relation between a case when $k=1$, $k\ge 2$ 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.

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Jozef J. Kratica, Aleksandar Lj. Savić, Zoran Lj. Maksimović. 2018-03-08. Some properties of $\{k\}$-packing function problem in graphs. https://arxiv.org/abs/1803.03147

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