Non-monochromatic Triangles in a 2-Edge-Coloured Graph

Abstract

Let $G=(V,E)$ be a simple graph and let $\{R,B\}$ be a partition of $E$. We prove that whenever $|E|+\min \{|R|,|B|\}>\left(\genfrac{}{}{0ex}{}{|V|}{2}\right)$, there exists a subgraph of $G$ isomorphic to $K_3$ which contains edges from both $R$ and $B$. We conjecture a natural generalization to partitions with more blocks.