Disjoint Total Dominating Sets in Near-Triangulations
Combinatorics
2022-05-16 v1 Discrete Mathematics
Abstract
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].
Cite
@article{arxiv.2205.06464,
title = {Disjoint Total Dominating Sets in Near-Triangulations},
author = {P. Francis and Abraham M. Illickan and Lijo M. Jose and Deepak Rajendraprasad},
journal= {arXiv preprint arXiv:2205.06464},
year = {2022}
}