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Bent Hamilton Cycles in d-Dimensional Grid Graphs (2003)

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by F. Ruskey , Joe Sawada
Venue:J. COMBIN
Citations:2 - 0 self
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BibTeX

@ARTICLE{Ruskey03benthamilton,
    author = {F. Ruskey and Joe Sawada},
    title = {Bent Hamilton Cycles in d-Dimensional Grid Graphs},
    journal = {J. COMBIN},
    year = {2003},
    volume = {10},
    pages = {1}
}

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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 different 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.

Citations

73 Hamilton paths in grid graphs - Itai, Papadimitriou, et al. - 1982
59 A survey of combinatorial Gray codes - Savage - 1997
7 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, Erdös - 1978
4 Binary gray codes with long bit runs - Goddyn, Gvozdjak - 2003
3 Transition restricted Gray codes, Electron - Bultena, Ruskey
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