4 problems

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…

Finitely bounded homogeneous CSP dichotomy conjecture. Exactly one of the following holds: either $\operatorname{Pol}(\mathbb A)$ has a uniformly continuous minion homomorphism to…