Dataset of non-isomorphic graphs being coloring types (K6-e,Km-e;n), 2<m<5, 1<n<R(K6-e,Km-e)

Description

For K6-e and Km-e graphs, the type coloring (K6-e,Km-e;n) is such an edge coloring of
the full Kn graph, which does not have the K6-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(K6-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 K6-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 (K6-e,Km-e;n) exist for n<R(K6-e,Km-e).

The dataset consists of:
a) 7 files containing all non-isomorphic graphs that are coloring types (K6-e,K3-e;n) for 1<n<9,
b) 15 files containing all non-isomorphic graphs that are coloring types (K6-e,K4-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_k6ekme.zip

28.5 MB, S3 ETag 1d46d0dd06c9228cd5d7fc40e34a6bc4-1, downloads: 35

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/z6c2-cj70

Verified by:

Gdańsk University of Technology

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