Dataset of non-isomorphic graphs being coloring types (K3-e,Km-e;n), 2<m<8, 1<n<R(K3-e,Km-e)

Description

For K3-e and Km-e graphs, the type coloring (K3-e,Km-e;n) is such an edge coloring of the full Kn graph,
which does not have the K3-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(K3-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 K3-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 (K3-e,Km-e;n) exist for n<R(K3-e,Km-e).

The dataset consists of:
a) 1 file containing all non-isomorphic graphs that are coloring types (K3-e,K3-e;n) for 1<n<3,
b) 3 files containing all non-isomorphic graphs that are coloring types (K3-e,K4-e;n) for 1<n<5,
c) 5 files containing all non-isomorphic graphs that are coloring types (K3-e,K5-e;n) for 1<n<7,
d) 7 files containing all non-isomorphic graphs that are coloring types (K3-e,K6-e;n) for 1<n<9,
e) 9 files containing all non-isomorphic graphs that are coloring types (K3-e,K7-e;n) for 1<n<11.

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_k3ekme_new.zip

4.5 kB, S3 ETag b089903873ca9ec77d4424ab34bbb362-1, downloads: 17

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

License:: 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:

10.34808/7rrf-ay46

Verified by:

Gdańsk University of Technology

Keywords

References

dataset Dataset of non-isomorphic graphs of the coloring types (K3,Km-e;n), 2<m<7, 1<n<R(K3,Km-e).

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