• Corpus ID: 173990950

$\beta$-Packing Sets in Graphs

  title={\$\beta\$-Packing Sets in Graphs},
  author={Benjamin M. Case and Evan Haithcock and Renu C. Laskar},
  journal={arXiv: Combinatorics},
A set $S\subseteq V$ is $\alpha$-dominating if for all $v\in V-S$, $|N(v) \cap S | \geq \alpha |N(v)|.$ The $\alpha$-domination number of $G$ equals the minimum cardinality of an $\alpha$-dominating set $S$ in $G$. Since being introduced by Dunbar, et al. in 2000, $\alpha$-domination has been studied for various graphs and a variety of bounds have been developed. In this paper, we propose a new parameter derived by flipping the inequality in the definition of $\alpha$-domination. We say a set… 

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