This web-page contains the coefficients, the matrices and the script that can be used to verify the correctness of the proof of Lemma 5 presented in the paper "A problem of Erdös and Sós on 3-graphs" authored by Roman Glebov, Daniel Kráľ and Jan Volec.

- verification script and data (gzip; the compressed size of the archive is 13M)
*Description of the files in the archive:***verify.sage**– the verification Sage script**extremal-7**– the densities of 7-vertex 3-graphs in the extremal limit (the 3-graphs are ordered as in the list of all K_{4}^{−}-free graphs generated by flagmatic 1.5.1, see below)**flags.rat**– the pairing densities for types σ_1, …, σ_8 (generated by flagmatic 1.5.1)**ineq1**and**ineq2**– the inequalities (4) and (5) expressed as a combination of 7-vertex 3-graphs**gamma1**and**gamma2**– coefficients for the inequalities (4) and (5)**vectors_sigma1**, …,**vectors_sigma8**– list of vectors v^j_i for matrices A_1, …, A_8**weights_sigma1**, …,**weights_sigma8**– weights w^j_i of vectors v^j_i for matrices A_1, …, A_8

USAGE: run

*sage verify.sage*- Note that the computation requires around 7GB of memory and a 64bit version of Sage 5.x (tested with Sage 5.3 and 5.4.1).
- Also note that it takes between 45 and 60 minutes to run the computation (on Intel Core i7-3770 with 16GB RAM / AMD FX-8150 with 16GB RAM).

- Final vector generated by the script (gzip; the compressed size is 46M)
- list of 7-vertex graphs and flags rooted on σ_1, …, σ_8 (generated by flagmatic 1.5.1)