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For a graph $G$, let $\text{cg}(G)$ be the maximum $k\in \mathbb N$ for which $G$ contains a $k$-vertex cograph as an induced subgraph. The Erd\H{o}s-Hajnal conjecture asserts that for every proper hereditary graph class $\mathcal{G}$, there exists $\gamma\in(0,1]$ such that every $n$-vertex graph $G\in\mathcal{G}$ sat...
We prove a conjecture of Conlon, Fox, Gunby, He, Mubayi, Suk, Verstra\"{e}te, and Yu that for a $3$-graph $H$, the off-diagonal Ramsey number $R(H,n)$ is polynomial in $n$ if and only if $H$ is isomorphic to a subgraph of the"depth-$t$ iterated blowup"$\textsf{B}_t$ for an integer $t\geq 0$. Here, the $3$-graphs $\text...
<jats:p> A <jats:italic>bull</jats:italic> is a graph obtained from a four-vertex path by adding a vertex adjacent to the two middle vertices of the path. A graph <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">...
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