Minimising the number of triangular edges

TL;DR

This paper determines the exact minimum number of edges contained in triangles for large graphs with a fixed number of edges, confirming a conjecture by Furedi and Maleki.

Contribution

It proves a conjecture providing an exact formula for the minimum number of triangular edges in large graphs with a given edge count.

Findings

Exact formula for minimum triangular edges in large graphs

Confirmation of Furedi and Maleki's conjecture

Applicable to graphs with sufficiently large number of vertices

Abstract

We consider the problem of minimising the number of edges that are contained in triangles, among $n$-vertex graphs with a given number of edges. We prove a conjecture of F\"uredi and Maleki that gives an exact formula for this minimum, for sufficiently large $n$.