10 Problems for Partitions of Triangle-free Graphs

József Balogh, Felix Christian Clemen, Bernard Lidický

This page is containing computer assisted parts of the paper titled 10 Problems for Partitions of Triangle-free Graphs. A preliminary version of the paper can be downloaded here.

You can download the technical things as one archive

• anc.tar.gz (no generated files, 64KB)
• anc_all.tar.gz (all files, 6.9MB)

• 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
• pdflatex for checking input, optional

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

• run_all.sh ... shell script running everyhting
• run_lemma_X.Y.sh ... shell script to run the entire process for Lemma X.Y
• run_lemma_X.Y.transcript.txt ... generated when running
• rounding_Integer.sage ... SageMath tools for rounding semidefinite program
• Makefile ... for building the program creating semidefinite program
• flag_small.cpp ... program creating a semidefinite program
• F_edges2__forbidden.txt ... list of forbidden (induced) subgraphs, just $K_3$
• F_edges2__sizeK_typeXXX.txt ... list of flags on $K$ vertices of tyoe XXX. (generated)
• F_edges2__nX_labeled.txt ... list of labeled graphs on X vertices used in the calculation (generated)
• F_edges2__nX_sdp_products.txt ... part of SDP for faster reuse (generated)
• F_edges2__nX_unlabeled.txt ... list of all graphs on up to X vertices (generated)
• F_edges2__objective_XXX.txt ... Function to optimize and constraints (generated)
• SDP_nX_UB_F_3edges__objective_XXXX.txt.dat-s ... semidefinite program - input to csdp(generated)
• SDP_nX_UB_F_3edges__objective_XXXX.txt.dat-s.result ... numerical solution from csdp (generated)
• SDP_nX_UB_F_3edges__objective_XXXX.txt.dat-s.result.rounded.... ... rational solution from numerical one by SageMath (generated)
• SDP_nX_UB_F_3edges__objective_XXXX.txt.dat-s.log ... csdp solver output (generated)
• test_XXX ... latex drawing of the input constraints (generated)