3 problems

Let $c>0$. For a graph $H$ with at least one edge, define its congestion by … where the maximum is over subgraphs $J$ of $H$ with at least one edge; if $H$ has no edges, its conges…

A pure pair in a graph $G$ is a pair $A,B$ of disjoint vertex subsets such that $A$ is complete or anticomplete to $B$. A graph is perfect if every induced subgraph has chromatic n…

Forest–complement forest pure-pair conjecture. For every forest $H$, there exists $\varepsilon>0$ such that for every graph $G$ with $|G|>1$ that is both $H$-free and…