11 problems

Forbidden-minor characterization conjecture. The following are equivalent:

One-unit gap conjecture.

Equality conjecture.

Let $\mathcal{G}$ be a graph class. For graph parameters $\rho$ and $\omega$, say that $\mathcal{G}$ is $(\rho,\omega)$-bounded when bounded clique number in $\mathcal{G}$ implies…

Cameron's conjecture. For every graph $G$,

Brimkov's conjecture. For every integer $d\geq 2$,

Uncrossed-number separation conjecture. The uncrossed number can be arbitrarily far apart from the outerthickness. This conjecture asks whether the difference between these two gra…

Liu–Montgomery's crux conjecture. There exists some constant $c>0$ such that every graph $G$ contains a subdivision of a clique with at least

Let $G$ be a graph in the class of $P_7$-free bipartite graphs. The bounded symmetric-difference conjecture. The symmetric difference is bounded in the class of $P_7$-free bipartit…

$Z(d)$ conjecture. For odd $d\geq 21$,

Hliněný–Kwon–Obdržálek–Ordyniak conjecture. The class $\mathcal{C}$ has bounded rank-depth if and only if there exists an integer $t$ such that no graph $G\in\mathcal{C}$ contains…