In the paper Kochen-Specker set with seven contexts by Lisonek, Badziag, Portillo and Cabello, the following construction is used :

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Question : Have such constructions been used elsewhere, and if so what are recommended papers and books on that topic ?

Thank you.


This looks like a close relative of the Hamming graph: Vertices of the Hamming graph in question are $2-$element subsets of $\{1,\dots,7\}$. Edges join vertices corresponding to subsets intersecting in an element. Your graph is the Hamming graph with "overlaid edges" (two vertices are adjacent if they are on a straight segment).

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  • $\begingroup$ Thanks for this, it looks close indeed. And do you know if the linear algebra interpretation on top (finite lines as bases in particular) has been made a long time ago ? Thank you. $\endgroup$ – Thomas Sauvaget May 10 '15 at 4:14
  • $\begingroup$ An easy answer is: No. $\endgroup$ – Roland Bacher May 11 '15 at 12:30

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