Dataset of non-isomorphic graphs of the coloring types (Km,K3-e;n), 4<m<8, 1<n<R(Km,K3-e)

Description

For Km and K3-e graphs, a coloring type (Km,K3-e;n) is such an edge coloring of the full Kn graph, which does not have the Km subgraph in the first color (representing by no edges in the graph) or the K3-e subgraph in the second color (representing by edges in the graph). K3-e means the full Km graph with one edge removed.
The Ramsey number R(Km,K3-e) is the smallest natural number n such that for any edge coloring of the full Kn graph there is an isomorphic subgraph with Km in the first color (no edge in the graph) or isomorphic with K3-e in the second color (exists edge in the graph). Coloring types (Km,K3-e;n) exist for n<R(Km,K3-e).
The dataset consists of:
a) 7 files containing all non-isomorphic graphs that are coloring types (K5,K3-e;n) for 1<n<9,
b) 9 files containing all non-isomorphic graphs that are coloring types (K6,K3-e;n) for 1<n<11,
c) 11 files containing all non-isomorphic graphs that are coloring types (K7,K3-e;n) for 1<n<13.

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_kmk3e.zip

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CC BY

Attribution
Software:: Graph6 format

Details

Year of publication:

2020

Verification date:

2020-12-17

Dataset language:

English

Fields of science:

mathematics (Natural sciences)

DOI:

10.34808/k2a3-2h84

Verified by:

Gdańsk University of Technology

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