New blog post: Triply-Hamiltonian edge colorings
In https://mathstodon.xyz/@mjd/101098853869827835, Mark Jason Dominus (@mjd) observed that the regular dodecahedron can have its edges properly colored with three colors so that every two colors form a Hamiltonian cycle. In this post, I survey constructions for more graphs like this, and prove that no planar bipartite graph can have a coloring like this.
@christianp @11011110 What do you think? Better now? https://blog.plover.com/math/dodecahedral-3-coloring.html
@mjd @11011110 it looks like the kinds of edge are: solid black, blue dashes, blue dots.
I have protanopia, which is one of the kinds of colourblindness commonly called 'red-green'.
Using different colours makes sense, since it's a colouring problem, but getting even three colours that are good for everyone is tricky. Different patterns is the safest way to go, as you've done.
@christianp Can you please send me swatches or RGB triples for at least six colors that you find easily distinguishable?
@christianp Oh, and I just realized that the colored circles in the second diagram are not all going to be distinguishable. I will fix that.
@christianp If you don't mind, can you tell me which of these you prefer? (Please view at full size.)
@mjd in the first one, the circles are easily distinguished but hard to relate to the edges. In the second, it'd be much easier to see if the circles were filled with the pattern, instead of just around the edges
@christianp @mjd @11011110 I'd just like to point out that there do exist some well-tested resources for colourblind-friendly colour palettes. The most commonly recommended one is ColorBrewer (http://colorbrewer2.org/) by Cynthia Brewer: pick "qualitative" and "colorblind safe". I'm also partial to Paul Tol's colour schemes (https://personal.sron.nl/~pault/), which I find more aesthetically appealing. That said, I'm not colourblind, so I can't personally vouch for their effectiveness in that respect.
@christianp Are you red-green color blind? If so I would be grateful for your advice on any of my diagrams. I try to keep it in mind when I am designing, but I don't really know how well I am doing. But that dodecahedron diagram was a failure for everyone, including me.
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