20.500.12556/DiRROS-18189 Partial domination in supercubic graphs For some $\alpha$ with $0 < \alpha \le 1$, a subset $X$ of vertices in a graph $G$ of order $n$ is an $\alpha$-partial dominating set of $G$ if the set $X$ dominates at least $\alpha \times n$ vertices in $G$. The $\alpha$-partial domination number ${\rm pd}_{\alpha}(G)$ of $G$ is the minimum cardinality of an $\alpha$-partial dominating set of $G$. In this paper partial domination of graphs with minimum degree at least $3$ is studied. It is proved that if $G$ is a graph of order $n$ and with $\delta(G)\ge 3$, then ${\rm pd}_{\frac{7}{8}}(G) \le \frac{1}{3}n$. If in addition $n\ge 60$, then ${\rm pd}_{\frac{9}{10}}(G) \le \frac{1}{3}n$, and if $G$ is a connected cubic graph of order $n\ge 28$, then ${\rm pd}_{\frac{13}{14}}(G) \le \frac{1}{3}n$. Along the way it is shown that there are exactly four connected cubic graphs of order $14$ with domination number $5$. domination partial domination cubic graphs supercubic graphs dominacija delna dominacija kubični grafi superkubični grafi true false true Angleški jezik Slovenski jezik Neznano 2024-02-15 14:15:28 2024-02-15 14:15:28 2024-02-19 13:43:47 0000-00-00 00:00:00 2024 0 0 11 str. iss. 1, article no. 113669 Vol. 347 Jan. 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2024-01-01 519.17 0012-365X 10.1016/j.disc.2023.113669 162890243 https://www.sciencedirect.com/science/article/pii/S0012365X23003552 1 e9ca9eef-cbfb-11ee-aa6e-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=24699 1-s2.0-S0012365X23003552-main-1.pdf 1-s2.0-S0012365X23003552-main-1.pdf 1 ACE2EBE8F78937B8559A1EBDBF9D5E0F 8b294750627ec42929ad8eab5ff3d721eaaefd8bea7443fdb153fbc845ab3cb6 076669ce-cbfd-11ee-aa6e-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=24703 Inštitut za matematiko, fiziko in mehaniko 0 0 0