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Description
For K3 and Km-e graphs, a coloring type (K3,Km-e;n) is such an edge coloring of the full Kn graph, which does not have the K3 subgraph in the first color (representing by no edges in the graph) or the Km-e subgraph in the second color (representing by edges in the graph). Km-e means the full Km graph with one edge removed.
The Ramsey number R(K3,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 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,Km-e;n) exist for n<R(K3,Km-e).
The Ramsey number R(K3,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 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,Km-e;n) exist for n<R(K3,Km-e).
The dataset consists of:
a) 3 files containing all non-isomorphic graphs that are coloring types (K3,K3-e;n) for 1<n<5,
b) 5 files containing all non-isomorphic graphs that are coloring types (K3,K4-e;n) for 1<n<7,
c) 9 files containing all non-isomorphic graphs that are coloring types (K3,K5-e;n) for 1<n<11,
d) 15 files containing all non-isomorphic graphs that are coloring types (K3,K6-e;n) for 1<n<17.
a) 3 files containing all non-isomorphic graphs that are coloring types (K3,K3-e;n) for 1<n<5,
b) 5 files containing all non-isomorphic graphs that are coloring types (K3,K4-e;n) for 1<n<7,
c) 9 files containing all non-isomorphic graphs that are coloring types (K3,K5-e;n) for 1<n<11,
d) 15 files containing all non-isomorphic graphs that are coloring types (K3,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/).
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_k3kme.zip
28.1 kB,
S3 ETag
e2edc5915ecf342c32c041041728222f-1,
downloads: 89
The file hash is calculated from the formula
Example script for calculation:
https://github.com/antespi/s3md5
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
File details
- License:
-
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CC BYAttribution - Software:
- Graphs have been saved in Graph6 format
Details
- Year of publication:
- 2020
- Verification date:
- 2020-12-17
- Dataset language:
- English
- Fields of science:
-
- mathematics (Natural sciences)
- DOI:
- DOI ID 10.34808/wgmq-hd26 open in new tab
- Verified by:
- Gdańsk University of Technology
Keywords
References
- dataset Dataset of non-isomorphic graphs being coloring types (K3-e,Km-e;n), 2<m<8, 1<n<R(K3-e,Km-e)
- dataset Dataset of non-isomorphic graphs of the coloring types (Km,K3-e;n), 4<m<8, 1<n<R(Km,K3-e)
- dataset Dataset of non-isomorphic graphs of the coloring types (K3,Km;n), 2<m<7, 1<n<R(3,m)
- dataset Dataset of non-isomorphic graphs of the coloring types (K4,K4;n), 1<n<R(4,4)
- dataset Dataset of non-isomorphic graphs of the coloring types (K4,Km-e;n), 2<m<5, 1<n<R(K4,Km-e)
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