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ON THE LENGTH OF SNAKES IN POWERS OF COMPLETE GRAPHS

Published online by Cambridge University Press:  04 February 2005

JERZY WOJCIECHOWSKI
Affiliation:
Department of Mathematics, West Virginia University, PO Box 6310, Morgantown, WV 26506-6310, [email protected]
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Abstract

The conjecture stated in an earlier paper by the author that there is a constant $\lambda$ (independent from both $n$ and $k$) such that $S(K_{n}^{d})\ge \lambda n^{d-1}$ holds for every $n\ge 2$ and $d\ge 2$, where $S(K_{n}^{d})$ is the length of the longest snake (cycle without chords) in the Cartesian product $K_{n}^{d}$ of $d$ copies of the complete graph $K_{n}$, is proved.

Type
Notes and Papers
Copyright
The London Mathematical Society 2005

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