Disjoint Paired-Dominating sets in Cubic Graphs.
Gábor BacsóCsilla BujtásCasey TompkinsZsolt TuzaPublished in: 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.