### Graph Colouring with Group Theory

I tried to constrain myself to one page. This document shows a connection between graph theory and group theory, allowing one to transfer computability results from k-colouring to a certain class of problems in group theory. Unfortunately, due to the one page constraint, I did not make certain notions precise, but I hope the reader can still make out the main ideas.

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### Comments

I think that the author did a nice job of condensing the ideas of relating graph coloring and the symmetry group of the square, although the fact that it occupied only a single (albeit cleanly made) page meant that a lot of context that would help someone not familiar with the ideas was lacking. A figure of a graph with the mapping between the two ideas drawn explicitely may have also been a welcome addition.

3.5I an appreciate that the Motivation of this paper may lie outside of my maths realm (and hence I recognise my bias in not being able to score this component very well), however the Clarity component is clearly extremely low as it is not understandable with minimal background in Group Theory, and the entry reads more like a Group Theory proof than an SoME submission.

1.3I like the topic and layout, and the one-page challenge you set yourself. For me, the part starting with : "We then require..." up to the sentence "Turns out, ..." was a bit cryptic - perhaps the definition required too much space? Or maybe you just intended the reader to put in some effort her? As an alterative... just make the margins a bit narrower ;-) Otherwise, nice set up and very readable!

5I could understand it because i study this sort of math but i think it is to technically or to fast to for readers with only a highschool background (at least from a german standpoint). The visual were nicely done and clear. (Were was the 1 page constraint cuoldnt find it)

5A very cool short read for nerds (like meee) :3 though unfortunately things for a general audience score better for SoME

3.5I understand that there is some connection between colouring problem and certain groups but still can't see what is the benefit of changing concepts yet.

7.4Nice and short, but leaves me wondering "what's the point?". Would be nice if it had some sort of motivation, some reason that this actually matters. Stretching to a second page would not be a problem here, and it'd make everything less constrained.

4first impression - great visual design pictures with 'a' in "Definition" are a bit confusing - maybe arrows would be better? more explanation of that first equation in "The Connection" would be helpful - where did it come from? perhaps giving yourself a few more pages of space would allow you to make explanations more fleshed out

3.3