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Journal of the London Mathematical Society 1994 50(3):465-476; doi:10.1112/jlms/50.3.465
© 1994 by London Mathematical Society
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© The London Mathematical Society

Long Snakes in Powers of the Complete Graph with an Odd Number of Vertices

Jerzy Wojciechowski

Department of Mathematics, West Virginia University PO BOX 6310, Morgantown, West Virginia 26506-6310, USA E-mail: UN020243{at}VAXA.WVNET.EDU, JERZY{at}MATH.WVU.EDU

Received 6 October 1992.

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.


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