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Article Title
Abstract
In any graph $G$, the domination number $\gamma(G)$ is at most the independence number $\alpha(G)$. The \emph{Inverse Domination Conjecture} says that, in any isolate-free $G$, there exists pair of vertex-disjoint dominating sets $D, D'$ with $|D|=\gamma(G)$ and $|D'| \leq \alpha(G)$. Here we prove that this statement is true if the upper bound $\alpha(G)$ is replaced by $\frac{3}{2}\alpha(G) - 1$ (and $G$ is not a clique). We also prove that the conjecture holds whenever $\gamma(G)\leq 5$ or $|V(G)|\leq 16$.
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Recommended Citation
Krop, Elliot; McDonald, Jessica; and Puleo, Gregory J.
(2021)
"Upper bounds for inverse domination in graphs,"
Theory and Applications of Graphs: Vol. 8:
Iss.
2, Article 5.
DOI: 10.20429/tag.2021.080205
Available at:
https://digitalcommons.georgiasouthern.edu/tag/vol8/iss2/5
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