A Mathon-type construction for digraphs and improved lower bounds for Ramsey numbers

TL;DR

This paper introduces a new edge-colored digraph construction inspired by Mathon's method, linking it to power Paley digraphs, and uses this to establish improved lower bounds for multicolor directed Ramsey numbers.

Contribution

It presents a novel Mathon-type construction for digraphs and leverages it to enhance lower bounds for multicolor directed Ramsey numbers.

Findings

Constructed a new edge-colored digraph analogous to Mathon's construction.

Established a connection between the digraph and power Paley digraphs.

Produced improved lower bounds for multicolor directed Ramsey numbers.

Abstract

We construct an edge-colored digraph analogous to Mathon's construction for undirected graphs. We show that this graph is connected to the $k$-th power Paley digraphs and we use this connection to produce improved lower bounds for multicolor directed Ramsey numbers.