Best possible upper bounds on the restrained domination number of cubic graphsBrešar, Boštjan (Avtor) Henning, Michael A. (Avtor) dominationrestrained dominationcubic graphsA dominating set in a graph $G$ is a set $S$ of vertices such that every vertex in $V(G) \setminus S$ is adjacent to a vertex in $S$. A restrained dominating set of $G$ is a dominating set $S$ with the additional restraint that the graph $G - S$ obtained by removing all vertices in $S$ is isolate-free. The domination number $\gamma(G)$ and the restrained domination number $\gamma_{r}(G)$ are the minimum cardinalities of a dominating set and restrained dominating set, respectively, of $G$. Let $G$ be a cubic graph of order $n$. A classical result of Reed [Combin. Probab. Comput. 5 (1996), 277-295] states that $\gamma(G) \le \frac{3}{8}n$, and this bound is best possible. To determine a best possible upper bound on the restrained domination number of $G$ is more challenging, and we prove that $\gamma_{r}(G) \le \frac{2}{5}n$.20242024-06-18 10:12:40Neznano19113UDK: 519.17ISSN pri članku: 0364-9024DOI: 10.1002/jgt.23095COBISS_ID: 199137795sl