3 problems

Let $G$ be a planar graph, and let $\Delta(G)$ denote its maximum vertex degree and $b(G)$ its bondage number, the smallest number of edges whose removal increases the domination nu…

Let $\mathcal{P} \subseteq \mathcal{G}$ be additive and hereditary. A graph $G$ is vertex-$\gamma_{\mathcal{P}}$-critical if its vertex domination number with respect to…

Let $G$ be a connected graph of orientable genus $h$ and non-orientable genus $k$. Let $b(G)$ be its bondage number and $\Delta(G)$ its maximum vertex degree. Let $c_h$ and $c'_k$…