Hamiltonian Paths in Cartesian Powers of Directed Cycles
نویسندگان
چکیده
منابع مشابه
Hamiltonian Paths in Cartesian Powers of Directed Cycles
The vertex set of the kth cartesian power of a directed cycle of length rn can be naturally identified with the abelian group For any two elements u = (u l , . . . , uk) and v = (01,. . . , uk) of (z~), it is easy to see that if there is a hamiltonian path from u to u, then u\ + ~ ~ ~ + u i c = v 1 + Â ¥ . . + u k + (modrn). We prove the converse, unless k = 2 and rn is odd.
متن کاملHamiltonian Paths in Cartesian Powers of Directed Cycles
The vertex set of the k cartesian power of a directed cycle of length m can be naturally identified with the abelian group (Zm) . For any two elements v = (v1, . . . , vk) and w = (w1, . . . , wk) of (Zm) , it is easy to see that if there is a hamiltonian path from v to w, then v1 + · · ·+ vk ≡ w1 + · · ·+ wk + 1 (mod m). We prove the converse, unless k = 2 and m is odd.
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2003
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-002-0519-3