Hamiltonian Paths in Cartesian Powers of Directed Cycles

Details Hamiltonian Paths in Cartesian Powers of Directed Cycles Hamiltonian Paths in Cartesian Powers of Directed Cycles

2001-10-05

arxiv.org/abs/math/0110073v1

Mathematics

Combinatorics

8 pages, no figures

Scientific paper

The vertex set of the kth cartesian power of a directed cycle of length m can be naturally identified with the set of k-tuples of integers modulo m. For any two vertices v and w of this graph, it is easy to see that if there is a hamiltonian path from v to w, then the sum of the coordinates of v is congruent, modulo m, to one more than the sum of the coordinates of w. We prove the converse, unless k = 2 and m is odd.

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