Carlos Hoppen, Hanno Lefmann, Knut Odermann
Published 2020-04-24Version 1
In this note, we adapt the Keevash-Sudakov proof of the (Tur\'{a}n) Stability Theorem for the Fano plane to find an explicit dependency between the parameters $\varepsilon$ and $\delta$. This is useful in the solution of a multicolored version for hypergraphs of an extremal problem about edge-colorings, known as the Erd\H{o}s-Rothschild problem, which may be considered for the Fano plane.
Comments: 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
A new stability theorem for the expansion of cliques
Stability results on the circumference of a graph
Two stability theorems for $\mathcal{K}_{\ell + 1}^{r}$-saturated hypergraphs
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