We find necessary and sufficient conditions for the existence of a closed walk that traverses r vertices twice and the rest once in the Cayley digraph of 2, @ 2,. This is a generalization of the results known for r = 0 or 1. In 1978, Trotter and Erdos [3] gave a necessary and sufficient condition f
On the Hamiltonian cycle and the Hamiltonian chain in the Cartesian product of two graphs
β Scribed by K. A. Zaretskii
- Publisher
- Springer US
- Year
- 1968
- Tongue
- English
- Weight
- 629 KB
- Volume
- 2
- Category
- Article
- ISSN
- 1573-8337
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We show that the Cartesian product Z, x Z, of two directed cycles is hypo-Hamiltonian (Hamiltonian) if and only if there is a pair of relatively prime positive integers m and n with ma + nb = ab -1 (ma + nb = ab). The result for hypo-Hamiltonian is new; that for Hamiltonian is known. These are speci
The Cartesian product of two hamiltonian graphs is always hamiltonian. For directed graphs, the analogous statement is false. We show that the Cartesian product C,,, x C, , of directed cycles is hamiltonian if and only if the greatest common divisor (g.c.d.) d of n, and n, is a t least two and there
It is a simple fact that cubic Hamiltonian graphs have at least two Hamiltonian cycles. Finding such a cycle is NP-hard in general, and no polynomial-time algorithm is known for the problem of finding a second Hamiltonian cycle when one such cycle is given as part of the input. We investigate the co