Dataset of non-isomorphic graphs being coloring types (K4-e,Km-e;n), 2<m<7, 1<n<R(K4-e,Km-e) - Open Research Data - Bridge of Knowledge

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Dataset of non-isomorphic graphs being coloring types (K4-e,Km-e;n), 2<m<7, 1<n<R(K4-e,Km-e)

Description

For K4-e and Km-e graphs, the type coloring (K4-e,Km-e;n) is such an edge coloring of the full Kn graph, 
which does not have the K4-e subgraph in the first color (no edge in the graph) or the Km-e subgraph 
in the second color (exists edge in the graph). Km-e means the full Km graph with one edge removed.
The Ramsey number R(K4-e,Km-e) is the smallest natural number n such that for any edge coloring of the 
full Kn graph there is an isomorphic subgraph with K4-e in the first color (no edge in the graph) or isomorphic
 with Km-e in the second color (exists edge in the graph). Coloring types (K4-e,Km-e;n) exist for n<R(K4-e,Km-e).

The dataset consists of:
a) 3 files containing all non-isomorphic graphs that are coloring types (K4-e,K3-e;n) for 1<n<5,
b) 8 files containing all non-isomorphic graphs that are coloring types (K4-e,K4-e;n) for 1<n<10,
c) 11 files containing all non-isomorphic graphs that are coloring types (K4-e,K5-e;n) for 1<n<13,
d) 15 files containing all non-isomorphic graphs that are coloring types (K4-e,K6-e;n) for 1<n<17.

All graphs have been saved in Graph6 format (https://users.cecs.anu.edu.au/~bdm/data/formats.html).
The Nauty package by Brendan D. McKay was used to check the isomorphism of the graphs 
(http://users.cecs.anu.edu.au/~bdm/nauty/). 
We recommend the survey article of S. Radziszowski containing the most important results 
regarding Ramsey numbers: S. Radziszowski, Small Ramsey numbers, Electron. 
J. Comb. Dyn. Surv. 1, revision #15, DS1: Mar 3, 2017 ( https://doi.org/10.37236/21). 

 

Dataset file

dataset_k4ekme.zip
28.1 MB, S3 ETag d82955076cdb2cc1a9a9452c8b7e3463-1, downloads: 16
The file hash is calculated from the formula
hexmd5(md5(part1)+md5(part2)+...)-{parts_count} where a single part of the file is 512 MB in size.

Example script for calculation:
https://github.com/antespi/s3md5
download file dataset_k4ekme.zip

File details

License:
Creative Commons: by 4.0 open in new tab
CC BY
Attribution
Software:
Graph6 format

Details

Year of publication:
2021
Verification date:
2021-03-17
Dataset language:
English
Fields of science:
  • Mathematics (Natural sciences)
DOI:
DOI ID 10.34808/w6ma-y715 open in new tab
Verified by:
Gdańsk University of Technology

Keywords

References

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