3 problems

Let $G$ be the dual graph of an equivalence relation with countably many equivalence classes, each of countable size. For a closed subsemigroup $S$ of a full transformation monoid,…

Let $k$-clique-free graphs be graphs containing no complete subgraph on $k$ vertices, with the triangle-free case corresponding to $k=3$. Big Ramsey degrees measure the least numbe…

Let $\mathfrak{N}$ be the Covington graph, the countable graph described in the source via a dense codense colouring of $(\mathbb{Q},<)$. A Cayley graph is a graph obtained from a…