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Lower bounds on lengths of checking sequences

✍ Scribed by Guy-Vincent Jourdan; Hasan Ural; Hüsnü Yenigün; Ji Chao Zhang


Publisher
Springer
Year
2009
Tongue
English
Weight
191 KB
Volume
22
Category
Article
ISSN
0934-5043

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A strong node sequence for a directed graph G = (N, A) is a sequence of nodes containing every cycle-free path of G as a subsequence. A weak node sequence for G is a sequence of nodes containing every basic path in G as a subsequence, where a basic path nt, n~ ..... nj, is a path from Ilt to nk such

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✍ Shalom Eliahou 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 607 KB

## Eliahou, S., The 3x+ 1 problem: new lower bounds on nontrivial cycle lengths, Discrete Mathematics 118 (1993) 45556. Let 7': N -+ N be the function defined by T(n) = n/2 if n is even, T(n) = (3n + 1)/2 if n is odd. We show, among other things, that any nontrivial cyclic orbit under iteration o