4 problems

Polynomial-separator or bounded-hole conjecture. There exists a polynomial $p$ and an integer $k$ such that if $G$ has no clique cutset and does not contain $K_{2,3}$ as an induced…

A graph is a finite undirected graph, and a minimal separator is a vertex set that minimally separates some pair of vertices. Theta-pyramid-prism-turtle conjecture. There is a poly…

Let ${\cal F}$ be a hereditary class of graphs. A $k$-creature consists of four pairwise disjoint vertex sets $A$, $B$, $X=\{x_1,\ldots,x_k\}$, and $Y=\{y_1,\ldots,y_k\}$ such that…

For an integer $k \geq 3$, a graph $G$ is a $k$-creature if … such that $G[A]$ and $G[B]$ are connected, $A$ is anticomplete to $B$, for $i=1,\dots,k$, $x_i y_i\in E(G)$, $x_i$ has…