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].

翻译：我们显示,每个最小度为三度的简单平板近三角图中,至少有两组完全脱节的总占优势。该类包括除三角以外的所有简单的平板三角图。这证实了戈达德和亨宁的推测[极分散的颜色,J.图示理论,88 (2018) 174-191]。