# Decomposing graphs into edges and triangles

##
Daniel Král', Bernard Lidický, Taísa L. Martins, Yanitsa Pehova

This page contains computer assisted parts of the paper
Decomposing graphs into edges and triangles.

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.
* Dependencies*

* Description of the content of tile23_computations.zip*

` F_edges2__n7_labeled.txt ` ... Flags $\vec{F} = (F_1,F_2,\ldots,F_7)$
` F_edges2__n7_unlabeled.txt ` ... $\mathcal{F}_7$ (generated file)
` F_edges2__objective.txt ` ... $\pi_{3,f}(U)$ (generated file)
` Makefile ` ... for compilation of `flag_small.cpp`
` SDP_n7_UB_F_edges2__objective.txt.dat-s ` ... semidefinite program minimizing $max_U \{ \pi_{3,f}(U) + c_U \}$ (generated file)
` SDP_n7_UB_F_edges2__objective.txt.dat-s.result ` ... solution of `SDP_n7_UB_F_edges2__objective.txt.dat-s` obtained by CSDP (generated file)
` flag_small.cpp ` ... C++ program generating `F_edges2__n7_unlabeled.txt` and `SDP_n7_UB_F_edges2__objective.txt.dat-s`
` generate_objective.sage ` ... Sage program generating `F_edges2__objective.txt`
` readme.txt ` ... Short description
` round.sage ` ... Sage program for turning `SDP_n7_UB_F_edges2__objective.txt.dat-s.result` into exact result
` rounding_exact.py ` ... Utilities used by `round.sage`
` run.output.txt ` ... output generated by running `run.sh`
` run.sh ` ... script to perform the entire calculation including compilation of `flag_small.cpp`
` check_M.sage ` ... script to check that $M$ presented in the paper is correct.