A note on a stability result for the Fano plane

Abstract

In this note, we adapt the Keevash-Sudakov proof of the (Turán) Stability Theorem for the Fano plane to find an explicit dependency between the parameters $\epsilon$ and $\delta$. This is useful in the solution of a multicolored version for hypergraphs of an extremal problem about edge-colorings, known as the Erdős-Rothschild problem, which may be considered for the Fano plane.

This article has been posted to give support to results about edge-coloring of 3-uniform hypergraphs that do not contain a copy of the Fano plane