11 problems

Vertex-minor Ramsey number conjecture for $k=5$.

Vertex-minor universality conjecture. If

A graph class is vertex-minor-closed if it contains every vertex-minor of each of its graphs. Geelen's simulation conjecture. Measurement-based quantum computation (MBQC) is effici…

Let $p=\omega(1/\sqrt n)$ with $p\leq 1/2$, and let $G$ be sampled from either $\mathbb{G}(n,p)$ or $\mathbb{G}(n,1-p)$. A graph is $k$-vertex-minor universal if every graph on any…

Kanté and Kwon's conjecture. A vertex-minor-closed class of graphs has bounded linear rank-width if and only if it does not contain some tree.

Let $G$ be an $n$-vertex circle graph, and let $\operatorname{CZ}(G)$ denote its CZ-distance. Circle-graph lower-bound conjecture. There exist $n$-vertex circle graphs $G$ with … T…

Let $d53d$ be a proper vertex-minor-closed class of graphs. For $k,p displaymath in \mathbb{N}$, a graph is $k$-rank-connected if it has at least $2k$ vertices and satisfies … f…

Kanté and Kwon's conjecture. For every tree $T$, the class of $T$-vertex-minor-free graphs has bounded linear rank-width.

Kanté–Kwon conjecture. For every fixed forest $T$, there is an integer $f(T)$ such that every graph of linear rank-width at least $f(T)$ contains a vertex-minor isomorphic to $T$.

Let $H$ be a graph. A class of graphs is $\chi$-bounded if there exists a function $f:\mathbb N\rightarrow\mathbb N$ such that for every graph $G$ in the class and every induced su…

Shrub-depth characterization conjecture. The class $\mathcal{C}$ is of bounded shrub-depth if, and only if, there exists an integer $t$ such that no graph $G\in\mathcal{C}$ contain…