Snakes and pseudo-snakes in powers of complete graphs
نویسندگان
چکیده
منابع مشابه
On the Length of Snakes in Powers of Complete Graphs
We prove the conjecture stated in [10] that there is a constant λ (independent from both n and k) such that S(K n) ≥ λnd−1 holds for every n ≥ 2 and d ≥ 2, where S(K n) is the length of the longest snake (cycle without chords) in the Cartesian product K n of d copies of the complete graph Kn.
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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 c3 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 cnn ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1988
ISSN: 0012-365X
DOI: 10.1016/0012-365x(88)90036-2