This repository provides a working environment needed to reproduce calculations described in the arXiv preprint "Cayley graphs of order kp are hamiltonian for k < 48" by Dave Witte Morris and Kirsten Wilk (https://arxiv.org/abs/1805.00149).
It uses the Docker container with the latest public release of GAP with added LKH - a C implementation of the Lin-Kernighan heuristic for solving the traveling salesman problem (http://akira.ruc.dk/~keld/research/LKH/) by Keld Helsgaun. The container is maintained in a separate repository at https://github.com/alex-konovalov/gap-docker-lkh.
The gap directory contains the GAP source code and Jupyter notebooks,
and the log directory contains output files. The GAP input and output
code from https://arxiv.org/src/1805.00149v1/anc was used to initialise
this repository.
To use the code on Binder (https://mybinder.org/), perform the following steps:
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Click on the "launch binder" badge in this README file on GitHub, or open https://mybinder.org/v2/gh/alex-konovalov/hamiltonian-cayley-graphs/master in your browser.
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First "Loading repository: alex-konovalov/hamiltonian-cayley-graphs/master" will be displayed, followed by a non-interactive preview. When the environment will be ready, you will see the main Jupyter screen with a list of files.
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Click on any
.ipynbfile to open it. This will start GAP Jupyter notebook. You should be able to run the code in the notebook, e.g. by executing one cell after another, or by running all cells, and perform other actions, e.g. add new cells to the notebook, or start a new notebook. Your changes will not be preserved after the window will be closed, but you should be able to download the notebook in various formats. For further information about Jupyter, see https://jupyter-notebook-beginner-guide.readthedocs.io/en/latest/index.html.
Note that GitHub renders Jupyter notebooks in a human readable form, see e.g. https://github.com/alex-konovalov/hamiltonian-cayley-graphs/blob/master/gap/4-5-Valence2.ipynb.