Gujgiczer Anna: Domination and packing in graphs

A dominating set in a graph $G$ is a vertex set whose closed
neighborhoods cover all vertices of $G$, while a packing is a vertex set
whose closed neighborhoods are pairwise disjoint. The minimum size of a
dominating set is the domination number $\gamma(G)$, and the maximum
size of a packing is the packing number $\rho(G)$. Since every vertex in
the dominating set can dominate at most one vertex of a packing, we
always have the inequality $\rho(G)\leq \gamma(G)$. Small examples
already show that the two parameters are not equal in general. In this
talk we investigate graph classes for which the ratio
$\gamma(G)/\rho(G)$ is bounded by a constant, and classes for which no
such bound exists.

The talk is based on joint work with Ákos Dúcz.