A note on dense bipartite induced subgraphs

TL;DR

This paper provides a concise proof of a recent result showing that triangle-free graphs with high minimum degree necessarily contain dense bipartite induced subgraphs, highlighting structural properties of such graphs.

Contribution

It offers a simplified and streamlined proof of a known bound on the average degree of bipartite induced subgraphs in triangle-free graphs.

Findings

Triangle-free graphs with minimum degree d contain bipartite induced subgraphs with average degree Ω(ln d / ln ln d)

The proof simplifies understanding of the structure of high-degree triangle-free graphs

Supports the existence of dense bipartite structures in sparse triangle-free graphs

Abstract

This exposition contains a short and streamlined proof of the recent result of Kwan, Letzter, Sudakov and Tran that every triangle-free graph with minimum degree $d$ contains an induced bipartite subgraph with average degree $\Omega(\ln d/\ln\ln d)$.