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 the older longer version here or from arXiv.

Here, you can download the technical things as one archive

tile23_computations.zip (zip, around 150KB)

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

Some C++ compiler
Sage
CSDP

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.