# 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

Other (pre)requisites for redoing the entire calculation
- 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)

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