Long Snakes in Powers of the Complete Graph with an Odd Number of Vertices
Jerzy Wojciechowski · Journal of the London Mathematical Society · 1994
In [5] Abbott and Katchalski ask if there exists a constant c < 0 such that for every d ⩾ 2 there is a snake (cycle without chords) of length at least c3d in the product of d copies of the complete graph K3. We show that the answer to the above question is positive, and that in general for any odd integer n there is a constant cn such that for every d ⩾ 2 there is a snake of length at least cn nd in the product of d copies of the complete graph Kn.