The minimum number of triangular edges and a symmetrization method for multiple graphs

TL;DR

This paper derives an asymptotic formula for the minimum number of triangular edges in graphs with given vertices and edges, using a generalized symmetrization method for multiple graphs.

Contribution

It introduces a novel generalization of Zykov's symmetrization technique applicable to multiple graphs simultaneously.

Findings

Provides an asymptotic formula for triangular edges in graphs.

Develops a new symmetrization method for multiple graphs.

Enhances understanding of graph structures with minimal triangles.

Abstract

We give an asymptotic formula for the minimum number of edges contained in triangles in a graph having n vertices and e edges. Our main tool is a generalization of Zykov's symmetrization method that can be applied for several graphs simultaneously.