Disjoint Paired-Dominating sets in Cubic Graphs
Gábor Bacsó, Csilla Bujtás, Casey Tompkins, Źsolt Tuza · Graphs and Combinatorics · 2019
A paired-dominating set of a graph G is a dominating set D with the additional requirement that the induced subgraph G [ D ] contains a perfect matching. We prove that the vertex set of every claw-free cubic graph can be partitioned into two paired-dominating sets.