Python 3 code for dealing with finite, simple graphs. Allows for computation of defective Ramsey numbers and associated extremal graphs.
This package is a companion to Defective Ramsey Numbers and Cocolorings on Some Subclasses of Perfect Graphs by Yunus Emre Demirci, Tınaz Ekim and Mehmet Akif Yıldız
Package repository: https://github.com/yunusdemirci/DefectiveRamsey
In its current form, DefectiveRamsey requires that the user be at least somewhat familiar with Python and/or a Unix-derived shell or similar command-line interface.
DefectiveRamsey consists of executable program (defectiveramsey.py
) and two importable libraries used by these (isograph.py
, gengraph.py
). All are intended for use with Python 3. One of them (isograph.py
) taken from GraphR can be found https://github.com/ggchappell/GraphR . Please read https://github.com/ggchappell/GraphR/blob/master/LICENSE .
To compute the _defective Ramsey number at stated subclass R^C_k(a, b), run defectiveramsey.py
, passing k, a, b, C as command-line arguments. k, a, b represent numbers and C represents string.
> defectiveramsey.py 1 4 7 "bip"
To compute the _defective Ramsey number at stated subclass with initial base graphs R^C_k(a, b), add initial base graphs to "base.txt" and run defectiveramsey.py
, passing k, a, b, C as command-line arguments. k, a, b represent numbers and C represents string.
> defectiveramsey.py --base 1 4 7 "bip"
C represents graph subclass. We just implement for two graph subclass. "bip": can be used for bipartite graphs "pg": can be used for perfect graphs "all": can be used for all graphs without restriction.
*See the individual files for API documentation. Data formats are described in
isograph.py
.
isograph.py
-- Importable module. Functions for dealing with simple graphs & graph isomorphism.gengraph.py
-- Importable module. Functions for finding defective Ramsey numbers & related extremal graphs. Requiresisograph.py
.defectiveramsey.py
-- Executable program. Computes defectve Ramsey numbers. Requiresisograph.py
andgengraph.py
.RESULTS
-- Subdirectory for text files holding output ofdefectiveramsey.py
. Files namedR^*_#def_#dense_#sparse.txt
, where#
represents a integer, and*
represents a string. The numbers in the filename are the command-line parameters. For example, fileR^BIP_1def_4dense_4sparse.txt
holds the output from the commanddefectiveramsey.py 1 4 4 "bip"
.Defective Cocoloring
. All executable programs and results for defective cocoloring version. For detailed information, please readREADME.md
file in subdirectoryREADME.md
-- This file.