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A note on insecure 3-Colorings of graph vertices

Posted 3 months ago
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WOLFRAM MATERIALS for the ARTICLE:

Robert Cowen (2021).

Mixing Numbers and Unfriendly Colorings of Graphs.

The Mathematica Journal, 23.

https://doi.org/10.3888/tmj.23-4

Full article in PDF.

The Mathematica language has a robust set of built-in functions for graph theory explorations. Many of them come from the old Combinatorica package developed by Steven Skiena. However there is not much that deals with graph coloring. Out of necessity, I have created my own functions and have recently published a paper in The Mathematica Journal and I am adding a notebook with additional material here. Hopefully this will be useful to researchers in graph theory and encourage others to develop additional useful material for those interested in graph theory coloring problems.

POSTED BY: Robert Cowen
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enter image description here -- you have earned Featured Contributor Badge enter image description here Your exceptional post has been selected for our editorial column Staff Picks http://wolfr.am/StaffPicks and Your Profile is now distinguished by a Featured Contributor Badge and is displayed on the Featured Contributor Board. Thank you!

POSTED BY: Moderation Team

Thanks for this honor! I should also like to thank George Beck who was the editor for my Mathematica Journal articles and who has taught me much about the Mathematica programming language.

POSTED BY: Robert Cowen

If you work with graphs and colourings in Mathematica, you may find the IGraph/M package interesting. It has had very competitive graph colouring functionality for many years now, and also provides most graph-related functionality from the old Combinatorica, but in a much more performant way.

Needs["IGraphM`"]

PetersenGraph[VertexSize -> Large, EdgeStyle -> Thickness[0.05]] // 
  IGVertexMap[ColorData[97], VertexStyle -> IGMinimumVertexColoring] //
  IGEdgeMap[ColorData[99], EdgeStyle -> IGMinimumEdgeColoring]

POSTED BY: Szabolcs Horvát
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