Solving Turán's Tetrahedron Problem for the $\ell_2$-Norm

József Balogh, Felix Christian Clemen, Bernard Lidický

This page is containing computer assisted parts of the paper titled Solving Turán's Tetrahedron Problem for the $\ell_2$-Norm. A preliminary version of the paper can be downloaded here.

You can download the technical things as one archive

• anc.zip (zip, around 4MB)

• Sage Math for transforming numerical solution to an rational solution - getting an actual proof
• C++ compiled on MacOSX or Linux rebuilding the program for creating semidefinite program
• CSDP solved for semidefinite programs

Description of the files in anc.zip The archive contains three subdirectoris codegreesquared_F33, codegreesquared_K4, and codegreesquared_K5 and each contains data for one calculation. Below we provide description of files that appear in the main directory and subdirectories.

• rounding_exact.sage ... shared Sage providing tools for rounding semidefinite program
• F_3edges__forbidden.txt ... list of forbidden (induced) subgraphs
• F_3edges__n6_labeled.txt ... list of labeled 3-graphs on 6 vertices used in the calculation
• F_3edges__n6_unlabeled.txt ... list of all 3-graphs on up to 6 vertices
• F_3edges__objective.txt ... Function to optimize - sum of codegree squared
• Makefile ... for building the program creading semidefinite program
• SDP_n6_UB_F_3edges__objective.txt.dat-s ... semidefinite program - input to csdp
• SDP_n6_UB_F_3edges__objective.txt.dat-s.result ... numerical solution from csdp
• altered*.dat-s ... projection of the semidefinite program
• altered*.dat-s.result ... numerical solution projection of the semidefinite program from csdp
• altered*.dat-s.linear_solution.sage ... rational solution - this is the actual solution - certificate for the actual proof
• round.sage ... script for rounding SDP_n6_UB_F_3edges__objective.txt.dat-s into altered*.dat-s.linear_solution.sage
• run.sh ... shell script to run the entire process
• transcript.txt ... output of run.sh