A Purely Entropic Approach to the Rainbow Triangle Problem

TL;DR

This paper provides an entropic proof establishing an upper bound on the number of rainbow triangles in a 3-edge-colored graph based on the product of the counts of each color.

Contribution

It introduces a novel purely entropic method to prove an upper bound on rainbow triangles, offering a new perspective in combinatorial graph theory.

Findings

Upper bound of rom the number of rainbow triangles

Application of entropic methods in combinatorics

Simplified proof technique for rainbow triangle bounds

Abstract

In this short note, we present a purely entropic proof that in a $3$-edge-colored simple graph with $R$ red edges, $G$ green edges, and $B$ blue edges, the number of rainbow triangles is at most $\sqrt{2RGB}$.