## CNF Ramsey

Creates problem statements about Ramsey's theorem in CNF in the DIMACS format.  Blog post [here](https://jgh.xyz/posts/cnf_ramsey).

## Requirements

This program is written in Rust.

[inline-python](https://docs.rs/inline-python/latest/inline_python/) requires Python 3.10 specifically.  Newer versions of Python don't work.  I plan to remove this dependency at some point for this reason.

## Use

`cargo run --release <clique size> <complete graph size> <output filename>`

Example: `cargo run --release 4 17 out.cnf`

The generated file can be passed to a SAT solver, like [cryptominisat](https://github.com/msoos/cryptominisat).  The SAT solver will either find that the statement is satisfiable and produce a counterexample, or that the statement isn't satisfiable.  If the statement is satisfiable, `R(r,r) > n`.  If the statement is not satisfiable, `R(r,r) <= n`.

This program will also print a labelling of the edges of the complete graph.  Any labelling of the vertices can be chosen.