Dataset of non-isomorphic graphs of the coloring types (K4,K4;n), 1<n<R(4,4)

Description

For K4 graph, a coloring type (K4,K4;n) is such an edge coloring of the full Kn graph, which does not have the K4 subgraph in the first color (representing by no edges in the graph) or the K4 subgraph in the second color (representing by edges in the graph).
The Ramsey number R(4,4) is the smallest natural number n such that for any edge coloring of the full Kn graph there is an isomorphic subgraph with K4 in the first color (no edge in the graph) or isomorphic with K4 in the second color (exists edge in the graph). Coloring types (K4,K4;n) exist for n<R(4,4).
The dataset consists of 14 files containing all non-isomorphic graphs that are coloring types (K4,K4;n) for 1<n<16.

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_k4k4.zip

17.3 MB, S3 ETag 296e1134d4cb2c62fb72e0653810ac17-1, downloads: 36

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CC BY

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Details

Year of publication:

2020

Verification date:

2020-12-17

Dataset language:

English

Fields of science:

mathematics (Natural sciences)

DOI:

10.34808/s5wa-aa30

Verified by:

Gdańsk University of Technology

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