An independent dominating set in the complement of a minimum dominating set of a tree

Henning, Michael A.; Löwenstein, Christian; Rautenbach, Dieter GND

We prove that for every tree $T$ of order at least $2$ and every minimum dominating set $D$ of $T$ which contains at most one endvertex of $T$, there is an independent dominating set $I$ of $T$ which is disjoint from $D$. This confirms a recent conjecture of Johnson, Prier, and Walsh.

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Henning, Michael A. / Löwenstein, Christian / Rautenbach, Dieter: An independent dominating set in the complement of a minimum dominating set of a tree. 2009.

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