genus
- 2019 Sorge2019
- page 10 : feedback edge set $k$ upper bounds genus by $\mathcal O(k)$ – Lemma 4.19. The feedback edge set number $f$ upper bounds the genus $g$. We have $g \le f$.
- https://en.wikipedia.org/wiki/Genus_(mathematics)#Graph_theory
- genus – The genus of a graph is the minimal integer $n$ such that the graph can be drawn without crossing itself on a sphere with $n$ handles.
- unknown
- feedback edge set $k$ upper bounds genus by $\mathcal O(k)$ – Removing $k$ edges creates a forest that is embeddable into the plane. We now add one handle for each of the $k$ edges to get embedding into $k$-handle genus.
- genus $k$ upper bounds book thickness by $f(k)$
- genus $k$ upper bounds twin width by $f(k)$
- planar upper bounds genus by a constant
- SchroderThesis
- page 23 : bounded genus does not imply bounded clique width – Proposition 3.17
- page 24 : bounded vertex cover does not imply bounded genus – Proposition 3.18
- page 26 : bounded genus does not imply bounded distance to perfect – Proposition 3.24
- page 30 : bounded bandwidth does not imply bounded genus – Proposition 3.27
- page 33 : bounded genus does not imply bounded distance to planar – Proposition 3.34