6 problems

Let $G$ be a bipartite graph, and let $t$ denote the number of guards in the eternal domination game. The decision problem $\textsc{Fast-Strategy}$ asks whether the guards have a s…

Let $P_n$ denote the path on $n$ vertices, let G\mathbin{\raisebox{0.3mm}{scriptstylesquare}}H denote the Cartesian product of graphs, let $\gamma(G)$ be the domination number,…

Let $G=(V,E)$ be a graph with $n$ vertices and no isolated vertices, and let $\rho_{\mathrm{m}}^{\infty}(G)$ denote its m-eternal eviction domination number. The m-eternal eviction…

Let $G$ be a connected graph on $n$ vertices, let $\Delta(G)$ denote its maximum degree, let $\theta(G)$ denote its clique covering number, and let $\gamma_c^{\infty}(G)$ denote it…

Let $G=(V,E)$ be a connected graph, let $H$ be a subgraph of $G$, and let $G[V\setminus V(H)]$ be the subgraph induced by the vertices outside $H$. Write $\delta(\cdot)$ for minimu…

Let $P_n$ denote the path on $n$ vertices, let $P_3\mathbin{\square}P_n$ be the Cartesian product grid graph, and let $\gamma_{\mathrm{m}}^{\infty}(G)$ denote its m-eternal dominat…