9 problems

Erdős–Hajnal–Rado conjecture. There is a constant $c>0$ such that

Song, Wei, Zhang, and Zhao's conjecture. For all $k\ge2$ and even $m\ge4$,

Zhao and Wei's conjecture. For all $k\ge2$ and $m\ge2$,

Mao, Wang, Magnant, and Schiermeyer's conjecture. For $k\ge2$,

Fox, Grinshpun, and Pach's conjecture. For positive integers $k$ and $p$,

Let $G$ be a graph with $m$ edges and no isolated vertices, and let $r_2(G;2)$ denote its two-colour Ramsey number. Erdős's edge-count conjecture. There is a constant $c$ such that…

A two-coloring of $K_{42}$ is a Ramsey coloring for $K_5$ if it contains no monochromatic $K_5$. Ramsey-coloring conjecture. The Ramsey number satisfies … and the at least $328$ kn…

Politeness conjecture. Every sufficiently large integer is polite. The paper explains that this would follow from natural, currently unproved growth assumptions for Ramsey numbers,…

Let $k\geq 10$ be an integer, and let $p$ and $q$ be integers satisfying $p\geq k+2$ and $q\geq k+1$. Write $r_k(p,q)$ for the smallest integer $n$ such that every red-blue colorin…