Transitive subtournaments of $k$-th power Paley digraphs and improved lower bounds for Ramsey numbers

Dermot McCarthy, Mason Springfield

Let $k\ge 2$ be an even integer. Let $q$ be a prime power such that $q\equiv k+1(\mathrm{mod}2k)$. We define the $\text{k-th power Paley digraph}$ of order $q$, $G_k(q)$, as the gr…