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Dec 27, 2013 at 10:33 vote accept Wolfgang
Dec 27, 2013 at 10:04 comment added joro OK. Here is a drawing for k=3: s27.postimg.org/wwx38t3w3/graph_k_3.png
Dec 27, 2013 at 9:55 comment added Wolfgang Yes modulo n, but the way I've written it, you don't even need that. I don't have time right now to add a diagram for say k=2 or k=3, but you can easily draw one. For checking that the edges (i,i+1) for i=0,...,n-2 aren't a-edges, it suffices to note that there are 2 H-cycles (symmetric to each other w.r.t. the vertical axis) which alternate essentially between diagonals of the n-gon and edges of it.
Dec 27, 2013 at 8:59 comment added joro You mean the chords are modulo n? Verified with program for small $k$.
Dec 26, 2013 at 14:15 history edited Wolfgang CC BY-SA 3.0
corrected typos
Dec 26, 2013 at 10:19 history answered Wolfgang CC BY-SA 3.0