Disjoint Total Dominating Sets in Near-Triangulations

05/13/2022

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by   P. Francis, et al.

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We show that every simple planar near-triangulation with minimum degree at least three contains two disjoint total dominating sets. The class includes all simple planar triangulations other than the triangle. This affirms a conjecture of Goddard and Henning [Thoroughly dispersed colorings, J. Graph Theory, 88 (2018) 174-191].