Message #2249

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] color graph
Date: Mon, 04 Jun 2012 22:26:16 -0500

I like how you laid out the graph, and how it emphasizes the special role
of the white face :) It’d also be cool to see a presentation of the graph
without intersections. That should be possible (embedded in 3D), though I
guess it wouldn’t be as nicely symmetrical as the one you made.

I searched around a little (on Google, Wikipedia, and Wolfram Alpha) to see
if there was a special name for this graph, or for the graph you get after
removing the red nodes, but did not have any luck. An interesting close
call to the latter was the Grotzsch
graph<http://en.wikipedia.org/wiki/Gr%C3%B6tzsch_graph>
.

For this tiling/coloring, we have 16 faces, 30 edges, and 15 vertices,
giving a Euler Characteristic of 1 (projective plane). Seems like a lot of
the asymmetrical colorings end up producing that topology.

Roice

On Mon, Jun 4, 2012 at 6:32 AM, Eduard <baumann@mcnet.ch> wrote:

>
>
> MT „hyp {5,4} 16 no e 0.5:0:0 v 1:0:0" has a very beautyful color
> graph! 16 no color graph<http://xa.yimg.com/kq/groups/10714925/tn/1867620670/name/color+graph+16no.jpg>
>
>
>
>