Inducibility of 4-vertex tournaments

Dalton Burke, Bernard Lidický, Florian Pfender, Michael Phillips

This page contains computer assisted parts of the paper Inducibility of 4-vertex tournaments.

A preliminary version of the paper can be downloaded here or from arXiv.

Here, you can download the technical things (certificates for flag algebra calculations) as one archive

• anc.tar.gz (tar.gz, around 50MB)

Dependencies

• Some C++11 compiler
• SageMath
• CSDP

Description of the content of anc.tar.gz
Lemma 1.3

• check.sh ... performs check of presented certifcates. Only SageMath is needed.
• recalculate.sh ... script performing the entire calculation (around 6 hours on Apple M1)
• claim_* ... directory containing certificate for claim *
• F_??__nX_labeled.txt ... List of labeled flags on X vertices
• F_??__nX_unlabeled.txt ... List of unlabeled flags on X vertices
• F_??__objective.txt ... objective function for min or max program and costriants
• SDP_nX_?B_.txt.dat-s ... semidefinite program
• SDP_nX_?B_.txt.dat-s.result ... semidefinite program - numerical solution by csdp
• SDP_nX_?B_.txt.dat-s.result.rounded.Integer.all.pkl ... semidefinite program - actual exact solution (certificate)
• altered*.. ... projection of semidefinite program
• rounding_Integer.sage ... sage script for approximate roundig
• rounding_exact.sage ... sage script for exact roundig
• round.sage ... performing rounding (making certificate)
• round.sage.log ... output when running round.sage
• check.sage ... tests the rounding (certificate)
• *.log ... output when running the script