Dataset of non-isomorphic graphs being coloring types (K5-e,Km-e;n), 2<m<5, 1<n<R(K5-e,Km-e)

Description

For K5-e and Km-e graphs, the type coloring (K5-e,Km-e;n) is such an edge coloring of the full Kn graph,
which does not have the K5-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(K5-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 K5-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 (K5-e,Km-e;n)
exist for n<R(K5-e,Km-e).

The dataset consists of:
a) 5 files containing all non-isomorphic graphs that are coloring types (K5-e,K3-e;n) for 1<n<7,
b) 11 files containing all non-isomorphic graphs that are coloring types (K5-e,K4-e;n) for 1<n<13.

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_k5ekme.zip

9.2 kB, S3 ETag f6a5964f958350b36df044a032154f92-1, downloads: 11

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

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File details

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CC BY

Attribution

Details

Year of publication:

2021

Verification date:

2021-03-17

Dataset language:

English

Fields of science:

mathematics (Natural sciences)

DOI:

10.34808/chgy-0e94

Verified by:

Gdańsk University of Technology

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