distance to complete
- 2022/09 Tran2022
- page 24 : distance to complete $k$ upper bounds edge clique cover number by $\mathcal O(k)$ – Proposition 4.2. Disatnce to Clique strictly upper bounds Edge Clique Cover Number.
- page 24 : bounded edge clique cover number does not imply bounded distance to complete – Proposition 4.2. Disatnce to Clique strictly upper bounds Edge Clique Cover Number.
- SchroderThesis
- page 16 : bounded distance to complete does not imply bounded maximum clique – Proposition 3.7
- page 16 : bounded distance to complete does not imply bounded domatic number – Proposition 3.7
- unknown
- complete upper bounds distance to complete by a constant – by definition
- distance to complete $k$ upper bounds clique cover number by $\mathcal O(k)$ – We cover the $k$ vertices of the modulator by cliques of size $1$ and cover the remaining clique by another one.
- distance to complete $k$ upper bounds edge clique cover number by $k^{\mathcal O(1)}$ – Cover the remaining clique, cover each modulator vertex and its neighborhood outside of it with another clique, cover each edge within the modulator by its own edge.