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
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:
-
open in new tabCC BYAttribution
- 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 10.34808/7rrf-ay46 open in new tab
- Verified by:
- Gdańsk University of Technology
Keywords
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