clique cover number

• 2022/09 Tran2022
  • page 40 : bounded twin-width does not imply bounded clique cover number – Proposition 6.7. Twin-width is incomparable to Clique Cover Number.
  • page 40 : bounded clique cover number does not imply bounded twin-width – Proposition 6.7. Twin-width is incomparable to Clique Cover Number.
• 2019 Sorge2019
  • page 11 : clique cover number $k$ upper bounds maximum independent set by $\mathcal O(k)$ – Lemma 4.26. The minimum clique cover number $c$ strictly upper bounds the independence number $\alpha$.
• https://en.wikipedia.org/wiki/Clique_cover
  • clique cover number – … is a partition of the vertices into cliques … A minimum clique cover is a clique cover that uses as few cliques as possible. The minimum $k$ for which a clique cover exists is called the clique cover number of the given graph.
• SchroderThesis
  • page 15 : bounded clique cover number does not imply bounded distance to perfect – Proposition 3.6
  • page 16 : bounded clique cover number does not imply bounded clique-width – Proposition 3.9
  • page 19 : bounded clique cover number does not imply bounded chordality – Proposition 3.11
• unknown
  • 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.