Author: Rahil Baber
E-Mail: rahilbaber@outlook.com

Some induced hypercube Turan density results produced for John Goldwasser and John Talbot on 2013/06/12.

The data files describe upper bounds (proved using Razborov's flag algebra method), for the maximum density
of an induced hypercube subgraph. The vertex and edge versions of the problem are provided.

Proof files are given as well as C++ source code that can be used to verify the results of the proof files.
There are two files labelled Non-Rigorous Bounds and Rigorous Bounds. In both cases the first column is just
a label to identify the problem being investigated so it can be cross-referenced in the Bounds files and the
Proof files (it typical takes the form of something like 4-3 the first number being the dimension of the
hyprecube, and the second number an arbitrary index). The last column is a description of the hypercube we
are calculating the induced Turan density for.

In the Non-Rigorous Bound file, the middle column is the result of doing the optimization with a high
precision solver where intermediate calculations are done to roughly 30 significant figures. Note that at
each step truncation occurs and so the final output is not rigorous.

In the Rigorous Bound file, the middle column shows a mathematically rigorous bound once decisions have been
made on how to turn the approximate floating point values into rational numbers. (Because different
decisions could have been made in how to convert the floats into rationals, which would result in a
different final upper bound, we provide the Non-Rigorous Bound file which shows the output of the solver in
its raw form.) In the case where there is a bracketed rational next to the decimal, the proof files show the
upper bound is the rational value (i.e. both the decimal and the rational value are valid proveable upper
bounds).