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05c35 (secondary)

Journal of the London Mathematical Society (1)

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ON THE LENGTH OF SNAKES IN POWERS OF COMPLETE GRAPHS
JERZY WOJCIECHOWSKI
Journal:

Journal of the London Mathematical Society / Volume 71 / Issue 1 / February 2005

Published online by Cambridge University Press:

04 February 2005, pp. 22-32

Print publication:

February 2005
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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.