ON THE LENGTH OF SNAKES IN POWERS OF COMPLETE GRAPHS

The conjecture stated in an earlier paper by the author that there is a constant λ (independent from both n and k) such that S(Kdn ) λnd−1 holds for every n 2 and d 2, where S(Kdn ) is the length of the longest snake (cycle without chords) in the Cartesian product Kdn of d copies of the complete graph Kn, is proved.