Total domination in plane triangulations [article]

M. Claverol, A. García, G. Hernández, C. Hernando, M. Maureso, M. Mora, J. Tejel
2020 arXiv   pre-print
A total dominating set of a graph G=(V,E) is a subset D of V such that every vertex in V is adjacent to at least one vertex in D. The total domination number of G, denoted by γ _t (G), is the minimum cardinality of a total dominating set of G. A near-triangulation is a biconnected planar graph that admits a plane embedding such that all of its faces are triangles except possibly the outer face. We show in this paper that γ _t (G) ≤⌊2n/5⌋ for any near-triangulation G of order n≥ 5, with two exceptions.
arXiv:2011.04255v1 fatcat:n45cfivy7beoznvlv5obz5rm5u