# Pentagons in triangle-free graphs

##
Bernard Lidický, Florian Pfender

This page contains computer assisted parts of the paper
*Pentagons in triangle-free graphs*.

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

Here, you can download the technical things as one archive

It is also possible to download programs needed to perform the calculation
from arXiv, however the arXiv version does not contain files
that are generated during the calculation due to size limitations on arXiv.
* Dependencies*

* Description of the content of anc.zip*

` F_edges2__forbidden.txt ` ... List of forbidden flags (i.e. triangle)
` F_edges2__n6_labeled.txt ` ... List of labeled flags $x_\sigma$, for Claim 6
` F_edges2__n6_unlabeled.txt ` ... List of unlabeled flags on 6 vertices $\mathcal{F}_6$, for Claim 6
` F_edges2__n8_labeled.txt ` ... List of labeled flags $x_\sigma$, for Claim 5
` F_edges2__n8_unlabeled.txt ` ... List of unlabeled flags on 8 vertices $\mathcal{F}_8$, for Claim 5
` F_edges2__obj_BIG_384.txt ` ... objective for Claim 6
` F_edges2__obj_BIG_8.txt ` ... objecive for Claim 5
` SDP_n6_LB_F_edges2__obj_BIG_384.txt.dat-s ` ... semidefinite program for Claim 6
` SDP_n6_LB_F_edges2__obj_BIG_384.txt.dat-s.result ` ... solution of the semidefinite program for Claim 6
` SDP_n8_LB_F_edges2__obj_BIG_8.txt.dat-s ` ... semidefinite program for Claim 5
` SDP_n8_LB_F_edges2__obj_BIG_8.txt.dat-s.result ` ... solution of the semidefinite program for Claim 5
` altered.dat-s ` ... first projection of program for Claim 6
` altered.dat-s.result ` ... solution to first projection of program for Claim 6
` altered2.dat-s ` ... second projection of program for Claim 6
` altered2.dat-s.result ` ... solution to second projection of program for Claim 6
` calculation.sage ` ... Tests if Claim 5 and 6 work
` flag_small.cpp ` ... C++ program generating flags and their products
` readme.txt ` ... some small comments
` round.sage ` ... rounding for Claim 6
` rounding_Integer.sage ` ... sage script for approximate rounding in Claim 5
` rounding_exact.py ` ... sage script for exact rounding
` run.sh ` ... one file to do everything