Speaker
Hyemin Kwon
(Ajou University)
Description
A dominating set of a graph $G$ is a set $S$ of vertices such that each vertex not in $S$ is adjacent to some vertex in $S$. The independent domination number of a graph $G$, denoted $i(G)$, is the minimum cardinality of a dominating set of $G$ which is also independent. In 2018, Abrishami and Henning showed that $i(G) \leq \frac{4}{11}|V(G)|$ for every cubic graph $G$ with girth at least 6.
In this talk, we present a result on the independent domination number of a cubic graph, which implies the aforementioned result. More precisely, we prove that if $G$ is a cubic graph without 4-cycles, then $i(G) \leq \frac{5}{14}|V(G)|$, and the bound is tight. This is based on joint work with Eun-Kyung Cho, Ilkyoo Choi and Boram Park.
