3.1.7. cnfformula.families.ramsey module

CNF Formulas for Ramsey-like statements

class PTNCmdHelper

Bases: object

Command line helper for PTN formulas

Methods

build_cnf(args)	Build a Ramsey formula according to the arguments
setup_command_line(parser)	Setup the command line options for PTN formula

static build_cnf(args)

Build a Ramsey formula according to the arguments

Arguments: - args: command line options

description = 'Bicoloring of N with no monochromatic Pythagorean Triples'

name = 'ptn'

static setup_command_line(parser)

Setup the command line options for PTN formula

Arguments: - parser: parser to load with options.

PythagoreanTriples(N)

There is a Pythagorean triples free coloring on N

The formula claims that it is possible to bicolor the numbers from 1 to \(N\) so that there is no monochromatic triplet \((x,y,z)\) so that \(x^2+y^2=z^2\).

Parameters:

N : int

size of the interval

Raises:

ValueError

Parameters are not positive integers

References

[1]	M. J. Heule, O. Kullmann, and V. W. Marek. Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. arXiv preprint arXiv:1605.00723, 2016.

class RamseyCmdHelper

Bases: object

Command line helper for RamseyNumber formulas

Methods

build_cnf(args)	Build a Ramsey formula according to the arguments
setup_command_line(parser)	Setup the command line options for Ramsey formula

static build_cnf(args)

Build a Ramsey formula according to the arguments

Arguments: - args: command line options

description = 'ramsey number principle'

name = 'ram'

static setup_command_line(parser)

Setup the command line options for Ramsey formula

Arguments: - parser: parser to load with options.

RamseyLowerBoundFormula(s, k, N)

Formula claiming that Ramsey number r(s,k) > N

Arguments: - s: independent set size - k: clique size - N: vertices