4 problems

For a graph $H$, an $H$-deletion-saturated graph is an $H$-free graph $G$ with $E(G)\neq\varnothing$ such that, for every $e\in E(G)$, the graph $G-e$ is not $H$-free. A graph $H$…

Let $k\ge2$ be an integer, let $K$ be a finite clique, and let $c$ be a $k$-colouring of the edges of $K$ such that there is an edge of every colour. A locally finite perturbation…

Let $k obreakge3$ be an integer, and let $H$ be a finite $k$-uniform hypergraph. A locally finite perturbation of a hypergraph is obtained by adding or removing edges in a loca…

Let $T$ be a finite tournament. A locally finite perturbation of a tournament is obtained by changing the direction of arcs in a locally finite set. Tournament perturbation conject…