5 problems

Asymptotic domatic-number conjecture. For every fixed real number $C\geq 1$,

Let $H$ be a connected graph, and let $\operatorname{Forb}(H)$ denote the class of graphs with no induced subgraph isomorphic to $H$. A graph class is DOM-bounded if its graphs hav…

Let $G$ be a graph, and let its fractional domatic number be the maximum value obtained by assigning weights to dominating sets so that the total weight covering each vertex is at…

Let $G_{m,n}$ denote the finite two-dimensional grid graph with dimensions $m$ and $n$, and let $d_k(G)$ be its $k$-distance domatic number. A graph is $k$-distance domatically-ful…

Let $G$ be a graph, and let the subgraph domatic number denote the maximum number of vertex-disjoint dominating sets in a subgraph of $G$. Computing the subgraph domatic number is…