domatic number
- 2022/09 Tran2022
- page 20 : bounded twin-cover number does not imply bounded domatic number – Parameter is unbounded for the graph class of cliques.
- https://mathworld.wolfram.com/DomaticNumber.html
- domatic number – The maximum number of disjoint dominating sets in a domatic partition of a graph $G$ is called its domatic number $d(G)$.
- unknown
- minimum degree $k$ upper bounds domatic number by $\mathcal O(k)$ – The vertex of minimum degree needs to be dominated in each of the sets. As the sets cannot overlap there can be at most $k+1$ of them.
- bounded complete does not imply bounded domatic number – Parameter is unbounded for the graph class of cliques.
- SchroderThesis
- page 16 : bounded distance to complete does not imply bounded domatic number – Proposition 3.7
- page 20 : bounded distance to co-cluster does not imply bounded domatic number – Proposition 3.12
- page 20 : bounded distance to bipartite does not imply bounded domatic number – Proposition 3.12
- page 30 : bounded bisection bandwidth does not imply bounded domatic number – Proposition 3.28