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

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.

• Type: Journal
• Year: 2010
• Where: APPML
• Authors: Michael A. Henning, Christian Löwenstein, Dieter Rautenbach
• Keywords: APPML 2010, Dominating Set, Tree