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Dec 9, 2014 at 22:25 comment added Fabian Meumertzheim Thank you very much for your answer! Do you think that there is a way to construct $L(m, k)$ out of the abstract graph $P(m, k)$, i.e. without having distinguished vertices $v_1, \dots, v_n$ or knowing the value of $k$? This is the connection I had in mind when asking this question and one that could make it possible to derive one classification result from the other.
Dec 9, 2014 at 17:11 history answered Allen Hatcher CC BY-SA 3.0