Bent Hamilton cycles in d-dimensional grid graphs, Electron [2 citations — 0 self]
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by F. Ruskey, Joe Sawada
J. Combin
http://www.combinatorics.org/Volume_9/PostScriptfiles/v9i1r46.ps
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Abstract:
A bent Hamilton cycle in a grid graph is one in which each edge in a successive pair of edges lies in a dierent dimension. We show that the d-dimensional grid graph has a bent Hamilton cycle if some dimension is even and d 3, and does not have a bent Hamilton cycle if all dimensions are odd. In the latter case, we determine the conditions for when a bent Hamilton path exists. For the d-dimensional toroidal grid graph (i.e., the graph product of d cycles), we show that there exists a bent Hamilton cycle when all dimensions are odd and d 3. We also show that if d = 2, then there exists a bent Hamilton cycle if and only if both dimensions are even. 1
Citations
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| 43 | A survey of combinatorial Gray codes – Savage - 1997 |
| 9 | Analysis of Algorithms for Listing Equivalence Classes of k-ary Strings Induced by Simple Group Actions – Proskurowski, Ruskey, et al. - 1998 |
| 7 | When the Cartesian product of directed cycles is Hamiltonian – Trotter, Erdos - 1978 |
| 3 | Binary Gray Codes with Long Bit Runs – Goddyn, L, et al. - 2003 |
| 2 | Transition Restricted Gray Codes, Electronic – Bultena, Ruskey - 1996 |
| 1 | A survey of combinatorial Gray codes, SIAM Review 39 – Savage - 1997 |
