Small Ramsey numbers for books, wheels and generalizations

Bernard Lidický, Gwen McKinley, Florian Pfender, Steven Van Overberghe

This page is containing computer assisted parts for upper bounds of the paper titled Small Ramsey numbers for books, wheels and generalizations. For obtaining lower bounds constructions see https://github.com/gwen-mckinley/ramsey-books-wheels or a local copy .

For verification of the lower bounds presented in the paper see constructions_verification.ipynb usable in SageMath.

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

You can download the technical things for upper bounds as one archive

• anc_GR_mini.tar.gz (almost no generated files, 11MB)
• anc_GR.tar.gz (all files, 8.2GB)

• 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
• The large archive comes with all the output and a script that reads and interprets it. Only shell is needed to run it.

Description of the files in anc_GR.tar.gz in below.

• constructions_verification.ipynb ... SageMath notebook for verification of the consutructions presented in the paper version in .tar.gz archives may be outdated.
• check.sh ... small bash script that reads log from rounding and prints the results
• rounding_Integer.sage ... SageMath tools for rounding semidefinite program
• Makefile ... for building the program creating semidefinite program
• flag.cpp ... program creating a semidefinite program
• F_edges*__forbidden.txt ... list of forbidden (induced) subgraphs
• F_edges*__nX_labeled.txt ... list of labeled graphs on X vertices used in the calculation (generated)
• F_edges*__nX_unlabeled.txt ... list of all graphs on up to X vertices (generated)
• F_edges*__objective.txt ... Function to optimize
• SDP_nX_LB_F_*edges*__objective.txt.dat-s ... semidefinite program - input to csdp(generated)
• SDP_nX_LB_F_*edges*__objective.txt.dat-s.result ... numerical solution from csdp (generated)
• SDP_nX_LB_F_*edges*__objective.txt.dat-s.result.rounded.... ... rational solution from numerical one by SageMath (generated)
• SDP_nX_LB_F_*edges*__objective.txt.dat-s.csdp.log ... csdp solver output (generated)
• round* ... scrips and outputs for rounding the semidefinite program.